Lean Kernel Arena / rpylean

Version: v2026.5.5 · 📄 Declaration · 🔗 Source

Test "bogus1"

Expected: ✋ reject · Size: 11.4 KB · Lines: 198 · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 14 ms · instructions: 21.2 M · max rss memory: 7.4 MB

stderr:

theorem thm : Eq (OfNat.ofNat 0) (OfNat.ofNat 1) := True.intro
                                                    ^^^^^^^^^^
                                                    has type
                                                      True
                                                    but is expected to have type
                                                      Eq (OfNat.ofNat 0) (OfNat.ofNat 1)
checked in 0.002123s

Test "cedar"

Expected: 👍 accept · Size: 728.6 MB · Lines: 13.4 M · lean4export: 3.1.0 · Lean: 4.26.0 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 1.3 m · instructions: 590.9 G · max rss memory: 14.1 GB

Test "constlevels"

Expected: ✋ reject · Size: 15.3 KB · Lines: 283 · lean4export: 3.1.0 · Lean: 4.29.0-rc2 · 📄 Declaration

Test result: ✋ rejected · exit code 1 · wall time: 22 ms · instructions: 22.1 M · max rss memory: 7.6 MB

stderr:

theorem _test : let x : Nat := Nat
                        ^^^
                        has type
                          Type
                        but is expected to have type
                          Nat
checked in 0.002130s

Test "cslib"

Expected: 👍 accept · Size: 1.2 GB · Lines: 22.8 M · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 1.6 m · instructions: 654.6 G · max rss memory: 14.1 GB

stderr:

theorem Std.DTreeMap.Internal.Impl.balanced_glue.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ {l : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {r : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {hl : Std.DTreeMap.Internal.Impl.Balanced l}, ∀ {hr : Std.DTreeMap.Internal.Impl.Balanced r}, ∀ {hlr : Std.DTreeMap.Internal.Impl.BalancedAtRoot (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)}, Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.glue l r hl hr hlr) := fun {α β l r hl hr hlr} ↦ Eq.mpr (id (congrArg (fun x ↦ Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) l hl hlr (fun hl hlr ↦ r) x)) (funext fun sz ↦ funext fun k ↦ funext fun v ↦ funext fun l' ↦ funext fun r' ↦ funext fun hl ↦ funext fun hlr ↦ congrArg (Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr fun hr hlr ↦ l) (funext fun sz' ↦ funext fun k' ↦ funext fun v' ↦ funext fun l'' ↦ funext fun r'' ↦ funext fun hr ↦ funext fun hlr ↦ ite_congr (Eq.refl (LT.lt sz sz')) (fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)))) fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))))))) (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.minView.match_3.splitter r (fun l hl hlr ↦ Eq l l → HEq hl hl → HEq hlr hlr → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) l hl hlr (fun hl hlr ↦ r) fun sz k v l' r' hl hlr ↦ Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr (fun hr hlr ↦ l) fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt sz sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))))) l hl hlr (fun hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id hr) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (fun size k' v' l' r' hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.glue.match_1.splitter size k' v' l' r' (fun r hr hlr ↦ Eq r r → HEq hr hr → HEq hlr hlr → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.glue.match_1 size k' v' l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr (fun hr hlr ↦ Std.DTreeMap.Internal.Impl.inner size k' v' l' r') fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt size sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner size k' v' l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))))) r hr hlr (fun hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (Eq.mpr (id (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1)) (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ And.intro left (And.intro left (And.intro left right))) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (fun sz' k' v' l'' r'' hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (Decidable.casesOn (Nat.decLt size sz') (fun h ↦ Eq.mpr (id (congrArg (Std.DTreeMap.Internal.Impl.Balanced) (if_neg h))) (of_eq_true (Std.DTreeMap.Internal.Impl.balanced_balanceRErase._simp_1 (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))))) fun h ↦ Eq.mpr (id (congrArg (Std.DTreeMap.Internal.Impl.Balanced) (if_pos h))) (of_eq_true (Std.DTreeMap.Internal.Impl.balanced_balanceLErase._simp_1 hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (Eq.refl r) (HEq.refl hr) (HEq.refl hlr))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (Eq.refl l) (HEq.refl hl) (HEq.refl hlr))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) r → (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) (Std.DTreeMap.Internal.Impl.inner size k v l r) r' hlb hlr
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.size_glue.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ {l : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {r : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {hl : Std.DTreeMap.Internal.Impl.Balanced l}, ∀ {hr : Std.DTreeMap.Internal.Impl.Balanced r}, ∀ {hlr : Std.DTreeMap.Internal.Impl.BalancedAtRoot (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)}, Eq (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.glue l r hl hr hlr)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)) := fun {α β l r hl hr hlr} ↦ Eq.mpr (id (congrArg (fun x ↦ Eq (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) l hl hlr (fun hl hlr ↦ r) x)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r))) (funext fun sz ↦ funext fun k ↦ funext fun v ↦ funext fun l' ↦ funext fun r' ↦ funext fun hl ↦ funext fun hlr ↦ congrArg (Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr fun hr hlr ↦ l) (funext fun sz' ↦ funext fun k' ↦ funext fun v' ↦ funext fun l'' ↦ funext fun r'' ↦ funext fun hr ↦ funext fun hlr ↦ ite_congr (Eq.refl (LT.lt sz sz')) (fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)))) fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))))))) (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.minView.match_3.splitter r (fun l hl hlr ↦ Eq l l → HEq hl hl → HEq hlr hlr → Eq (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) l hl hlr (fun hl hlr ↦ r) fun sz k v l' r' hl hlr ↦ Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr (fun hr hlr ↦ l) fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt sz sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r))) l hl hlr (fun hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (id (Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.minView._proof_5 r a))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (fun size k' v' l' r' hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.glue.match_1.splitter size k' v' l' r' (fun r hr hlr ↦ Eq r r → HEq hr hr → HEq hlr hlr → Eq (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.glue.match_1 size k' v' l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr (fun hr hlr ↦ Std.DTreeMap.Internal.Impl.inner size k' v' l' r') fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt size sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner size k' v' l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k' v' l' r')) (Std.DTreeMap.Internal.Impl.size r))) r hr hlr (fun hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (id (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr hlr right h ↦ Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.size_glue._proof_1_9 l' r' a) h hlr hlr right) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r'))) (HEq.refl right)) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (fun sz' k' v' l'' r'' hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (Decidable.casesOn (Nat.decLt size sz') (fun h ↦ Eq.mpr (id (congrArg (fun x ↦ Eq (Std.DTreeMap.Internal.Impl.size x) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k' v' l' r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'')))) (if_neg h))) (Eq.mpr (id (congrArg (fun x ↦ Eq x (HAdd.hAdd size sz')) (Eq.trans (Std.DTreeMap.Internal.Impl.size_balanceRErase (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (congrArg (fun x ↦ HAdd.hAdd (HAdd.hAdd x (OfNat.ofNat 1)) sz') (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))))) (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr hlr h right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr right hlr h h ↦ Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.size_glue._proof_1_11 l' r' l'' r'' a) h hlr right hlr h) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r'))) (HEq.refl right)) h hlr hlr h right) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l'') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r''))) (HEq.refl right)) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr))))) fun h ↦ Eq.mpr (id (congrArg (fun x ↦ Eq (Std.DTreeMap.Internal.Impl.size x) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k' v' l' r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'')))) (if_pos h))) (Eq.mpr (id (congrArg (fun x ↦ Eq x (HAdd.hAdd size sz')) (Eq.trans (Std.DTreeMap.Internal.Impl.size_balanceLErase hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (congrArg (HAdd.hAdd (HAdd.hAdd size (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))))) (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr hlr h right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr right hlr h h ↦ Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.size_glue._proof_1_10 l' r' l'' r'' a) h hlr right hlr h) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r'))) (HEq.refl right)) h hlr hlr h right) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l'') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r''))) (HEq.refl right)) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr)))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (Eq.refl r) (HEq.refl hr) (HEq.refl hlr))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (Eq.refl l) (HEq.refl hl) (HEq.refl hlr))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) r → (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) (Std.DTreeMap.Internal.Impl.inner size k v l r) r' hlb hlr
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)

Test "init"

Expected: 👍 accept · Size: 309.5 MB · Lines: 6.1 M · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 3.0 m · instructions: 957.1 G · max rss memory: 14.1 GB

Test "init-prelude"

Expected: 👍 accept · Size: 3.5 MB · Lines: 63.7 k · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 315 ms · instructions: 1.8 G · max rss memory: 96.7 MB

stderr:

checked in 0.287581s

Test "level-imax-leq"

Expected: ✋ reject · Size: 5.6 KB · Lines: 93 · lean4export: 3.1.0 · Lean: 4.29.0-rc1 · 📄 Declaration

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:

def down.{u, v} : Type (imax u v) → Sort (imax u v) :=
  fun x ↦ x
  ^^^^^^^^^
  has type
    Type (imax u v) → Type (imax u v)
  but is expected to have type
    Type (imax u v) → Sort (imax u v)
checked in 0.000550s

Test "level-imax-normalization"

Expected: ✋ reject · Size: 5.8 KB · Lines: 96 · lean4export: 3.1.0 · Lean: 4.26.0 · 📄 Declaration

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.4 MB

stderr:

def down.{v} : Type v → Sort v :=
  fun x ↦ x
  ^^^^^^^^^
  has type
    Type v → Type v
  but is expected to have type
    Type v → Sort v
checked in 0.000563s

Test "mathlib"

Expected: 👍 accept · Size: 5.2 GB · Lines: 100.0 M · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 3.0 m · instructions: 953.3 G · max rss memory: 14.1 GB

stderr:

theorem Lean.Grind.CommRing.Mon.revlexWF._unary.eq_def : ∀ (_x : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon), Eq (Lean.Grind.CommRing.Mon.revlexWF._unary _x) (PSigma.casesOn _x fun m₁ m₂ ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ x ↦ Ordering) m₁ m₂ (fun _ ↦ Ordering.eq) (fun p m ↦ Ordering.gt) (fun p m ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂))) Ordering.lt) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂)) Ordering.gt))) := fun _x ↦ id (Eq.trans (WellFounded.fix_eq Lean.Grind.CommRing.Mon.revlexWF._unary._proof_1 (fun _x a ↦ PSigma.casesOn _x (fun m₁ m₂ a ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) m₁ m₂ (fun _ x ↦ Ordering.eq) (fun p m x ↦ Ordering.gt) (fun p m x ↦ Ordering.lt) (fun pw₁ m₁ pw₂ m₂ x ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_2 pw₁ m₁ pw₂ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂)) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_3 pw₁ m₁ pw₂ m₂)) Ordering.lt) (Ordering.then (x (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_4 pw₁ m₁ pw₂ m₂)) Ordering.gt))) a) a) _x) (Eq.mpr (id (congrFun' (congrArg (Eq) (Eq.trans (_private.Init.Grind.Ring.CommSolver.0.PSigma.casesOn._arg_pusher (PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) (fun _x ↦ Ordering) Lean.Grind.CommRing.Mon.revlexWF._unary (fun _x y ↦ (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y _x) _x fun m₁ m₂ a ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) m₁ m₂ (fun _ x ↦ Ordering.eq) (fun p m x ↦ Ordering.gt) (fun p m x ↦ Ordering.lt) (fun pw₁ m₁ pw₂ m₂ x ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_2 pw₁ m₁ pw₂ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂)) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_3 pw₁ m₁ pw₂ m₂)) Ordering.lt) (Ordering.then (x (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_4 pw₁ m₁ pw₂ m₂)) Ordering.gt))) a) (congrFun' (congrArg (PSigma.rec) (funext fun fst ↦ funext fun snd ↦ _private.Init.Grind.Ring.CommSolver.0.Lean.Grind.CommRing.Mon.revlexWF.match_1._arg_pusher.{1, 1, 1} (fun m₁ x ↦ Ordering) (PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) (fun _x ↦ Ordering) Lean.Grind.CommRing.Mon.revlexWF._unary (fun m₁ m₂ y ↦ (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂)) fst snd (fun _ x ↦ Ordering.eq) (fun p m x ↦ Ordering.gt) (fun p m x ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ x ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_2 pw₁ m₁ pw₂ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂)) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_3 pw₁ m₁ pw₂ m₂)) Ordering.lt) (Ordering.then (x (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_4 pw₁ m₁ pw₂ m₂)) Ordering.gt)))) _x))) (PSigma.rec (fun m₁ m₂ ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ x ↦ Ordering) m₁ m₂ (fun _ ↦ Ordering.eq) (fun p m ↦ Ordering.gt) (fun p m ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂))) Ordering.lt) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂)) Ordering.gt))) _x))) (Eq.refl (PSigma.rec (fun m₁ m₂ ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ x ↦ Ordering) m₁ m₂ (fun _ ↦ Ordering.eq) (fun p m ↦ Ordering.gt) (fun p m ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂))) Ordering.lt) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂)) Ordering.gt))) _x))))
has type
  (p : Lean.Grind.CommRing.Power) → (m : Lean.Grind.CommRing.Mon) → (fun x ↦ (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) (Lean.Grind.CommRing.Mon.mult p m) x) m → ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk (Lean.Grind.CommRing.Mon.mult p m) (Lean.Grind.CommRing.Mon.mult p m)) → Ordering) → Ordering
but is expected to have type
  (p : Lean.Grind.CommRing.Power) → (m : Lean.Grind.CommRing.Mon) → (fun x ↦ (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) (Lean.Grind.CommRing.Mon.mult p m) x) m → (fun x ↦ (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) (Lean.Grind.CommRing.Mon.mult p m) x) (Lean.Grind.CommRing.Mon.mult p m)
theorem Lean.Grind.Linarith.Poly.combine._unary.eq_def : ∀ (_x : PSigma fun p₁ ↦ Lean.Grind.Linarith.Poly), Eq (Lean.Grind.Linarith.Poly.combine._unary _x) (PSigma.casesOn _x fun p₁ p₂ ↦ Lean.Grind.Linarith.Poly.combine.match_1.{1} (fun p₁ p₁ ↦ Lean.Grind.Linarith.Poly) p₁ p₂ (fun p₂ ↦ p₂) (fun p₂ ↦ p₂) fun a₁ x₁ p₁ a₂ x₂ p₂ ↦ cond (Nat.beq x₁ x₂) let a : Int := HAdd.hAdd a₁ a₂
cond (BEq.beq a (OfNat.ofNat 0)) (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk p₁ p₂)) (Lean.Grind.Linarith.Poly.add a x₁ (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk p₁ p₂))) (cond (Nat.blt x₂ x₁) (Lean.Grind.Linarith.Poly.add a₁ x₁ (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk p₁ (Lean.Grind.Linarith.Poly.add a₂ x₂ p₂)))) (Lean.Grind.Linarith.Poly.add a₂ x₂ (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk (Lean.Grind.Linarith.Poly.add a₁ x₁ p₁) p₂))))) := fun _x ↦ Eq.mpr (id (congrArg (fun x ↦ Eq (Lean.Grind.Linarith.Poly.combine._unary _x) (x _x)) (funext fun _x ↦ congrArg (PSigma.casesOn _x) (funext fun p₁ ↦ funext fun p₂ ↦ congrArg (Lean.Grind.Linarith.Poly.combine.match_1.{1} (fun p₁ p₁ ↦ Lean.Grind.Linarith.Poly) p₁ p₂ (fun p₂ ↦ wfParam p₂) fun p₂ ↦ wfParam p₂) (funext fun a₁ ↦ funext fun x₁ ↦ funext fun p₁ ↦ funext fun a₂ ↦ funext fun x₂ ↦ funext fun p₂ ↦ congrFun' (congrArg (cond (Nat.beq (wfParam x₁) (wfParam x₂))) (id (id (have_val_congr' (fun a ↦ cond (BEq.beq a (OfNat.ofNat 0)) (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk (wfParam p₁) (wfParam p₂))) (Lean.Grind.Linarith.Poly.add a (wfParam x₁) (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk (wfParam p₁) (wfParam p₂))))) (Eq.refl (wfParam (HAdd.hAdd (wfParam a₁) a₂))))))) (cond (Nat.blt (wfParam x₂) (wfParam x₁)) (Lean.Grind.Linarith.Poly.add (wfParam a₁) (wfParam x₁) (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk (wfParam p₁) (Lean.Grind.Linarith.Poly.add (wfParam a₂) (wfParam x₂) (wfParam p₂))))) (Lean.Grind.Linarith.Poly.add (wfParam a₂) (wfParam x₂) (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk (Lean.Grind.Linarith.Poly.add (wfParam a₁) (wfParam x₁) (wfParam p₁)) (wfParam p₂)))))))))) (Eq.trans (WellFounded.Nat.fix_eq (fun x ↦ PSigma.casesOn x fun p₁ p₂ ↦ HAdd.hAdd (SizeOf.sizeOf p₁) (SizeOf.sizeOf p₂)) (fun _x a ↦ PSigma.casesOn _x (fun p₁ p₂ a ↦ Lean.Grind.Linarith.Poly.combine.match_1.{1} (fun p₁ p₂ ↦ ((y : PSigma fun p₁ ↦ Lean.Grind.Linarith.Poly) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun p₁ p₂ ↦ HAdd.hAdd (SizeOf.sizeOf p₁) (SizeOf.sizeOf p₂)) y (PSigma.mk p₁ p₂) → Lean.Grind.Linarith.Poly) → Lean.Grind.Linarith.Poly) p₁ p₂ (fun p₂ x ↦ p₂) (fun p₂ x ↦ p₂) (fun a₁ x₁ p₁ a₂ x₂ p₂ x ↦ cond (Nat.beq x₁ x₂) let a : Int := HAdd.hAdd a₁ a₂
cond (BEq.beq a (OfNat.ofNat 0)) (x (PSigma.mk p₁ p₂) (Lean.Grind.Linarith.Poly.combine._unary._proof_1 a₁ x₁ p₁ a₂ x₂ p₂)) (Lean.Grind.Linarith.Poly.add a x₁ (x (PSigma.mk p₁ p₂) (Lean.Grind.Linarith.Poly.combine._unary._proof_1 a₁ x₁ p₁ a₂ x₂ p₂))) (cond (Nat.blt x₂ x₁) (Lean.Grind.Linarith.Poly.add a₁ x₁ (x (PSigma.mk p₁ (Lean.Grind.Linarith.Poly.add a₂ x₂ p₂)) (Lean.Grind.Linarith.Poly.combine._unary._proof_2 a₁ x₁ p₁ a₂ x₂ p₂))) (Lean.Grind.Linarith.Poly.add a₂ x₂ (x (PSigma.mk (Lean.Grind.Linarith.Poly.add a₁ x₁ p₁) p₂) (Lean.Grind.Linarith.Poly.combine._unary._proof_3 a₁ x₁ p₁ a₂ x₂ p₂))))) a) a) _x) (Eq.mpr (id (congrFun' (congrArg (Eq) (Eq.trans (_private.Init.Grind.Ordered.Linarith.0.PSigma.casesOn._arg_pusher (PSigma fun p₁ ↦ Lean.Grind.Linarith.Poly) (fun _x ↦ Lean.Grind.Linarith.Poly) Lean.Grind.Linarith.Poly.combine._unary (fun _x y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun p₁ p₂ ↦ HAdd.hAdd (SizeOf.sizeOf p₁) (SizeOf.sizeOf p₂)) y _x) _x fun p₁ p₂ a ↦ Lean.Grind.Linarith.Poly.combine.match_1.{1} (fun p₁ p₂ ↦ ((y : PSigma fun p₁ ↦ Lean.Grind.Linarith.Poly) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun p₁ p₂ ↦ HAdd.hAdd (SizeOf.sizeOf p₁) (SizeOf.sizeOf p₂)) y (PSigma.mk p₁ p₂) → Lean.Grind.Linarith.Poly) → Lean.Grind.Linarith.Poly) p₁ p₂ (fun p₂ x ↦ p₂) (fun p₂ x ↦ p₂) (fun a₁ x₁ p₁ a₂ x₂ p₂ x ↦ cond (Nat.beq x₁ x₂) let a : Int := HAdd.hAdd a₁ a₂
cond (BEq.beq a (OfNat.ofNat 0)) (x (PSigma.mk p₁ p₂) (Lean.Grind.Linarith.Poly.combine._unary._proof_1 a₁ x₁ p₁ a₂ x₂ p₂)) (Lean.Grind.Linarith.Poly.add a x₁ (x (PSigma.mk p₁ p₂) (Lean.Grind.Linarith.Poly.combine._unary._proof_1 a₁ x₁ p₁ a₂ x₂ p₂))) (cond (Nat.blt x₂ x₁) (Lean.Grind.Linarith.Poly.add a₁ x₁ (x (PSigma.mk p₁ (Lean.Grind.Linarith.Poly.add a₂ x₂ p₂)) (Lean.Grind.Linarith.Poly.combine._unary._proof_2 a₁ x₁ p₁ a₂ x₂ p₂))) (Lean.Grind.Linarith.Poly.add a₂ x₂ (x (PSigma.mk (Lean.Grind.Linarith.Poly.add a₁ x₁ p₁) p₂) (Lean.Grind.Linarith.Poly.combine._unary._proof_3 a₁ x₁ p₁ a₂ x₂ p₂))))) a) (congrFun' (congrArg (PSigma.rec) (funext fun fst ↦ funext fun snd ↦ _private.Init.Grind.Ordered.Linarith.0.Lean.Grind.Linarith.Poly.combine.match_1._arg_pusher.{1, 1, 1} (fun p₁ p₁ ↦ Lean.Grind.Linarith.Poly) (PSigma fun p₁ ↦ Lean.Grind.Linarith.Poly) (fun _x ↦ Lean.Grind.Linarith.Poly) Lean.Grind.Linarith.Poly.combine._unary (fun p₁ p₂ y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun p₁ p₂ ↦ HAdd.hAdd (SizeOf.sizeOf p₁) (SizeOf.sizeOf p₂)) y (PSigma.mk p₁ p₂)) fst snd (fun p₂ x ↦ p₂) (fun p₂ x ↦ p₂) fun a₁ x₁ p₁ a₂ x₂ p₂ x ↦ cond (Nat.beq x₁ x₂) let a : Int := HAdd.hAdd a₁ a₂
cond (BEq.beq a (OfNat.ofNat 0)) (x (PSigma.mk p₁ p₂) (Lean.Grind.Linarith.Poly.combine._unary._proof_1 a₁ x₁ p₁ a₂ x₂ p₂)) (Lean.Grind.Linarith.Poly.add a x₁ (x (PSigma.mk p₁ p₂) (Lean.Grind.Linarith.Poly.combine._unary._proof_1 a₁ x₁ p₁ a₂ x₂ p₂))) (cond (Nat.blt x₂ x₁) (Lean.Grind.Linarith.Poly.add a₁ x₁ (x (PSigma.mk p₁ (Lean.Grind.Linarith.Poly.add a₂ x₂ p₂)) (Lean.Grind.Linarith.Poly.combine._unary._proof_2 a₁ x₁ p₁ a₂ x₂ p₂))) (Lean.Grind.Linarith.Poly.add a₂ x₂ (x (PSigma.mk (Lean.Grind.Linarith.Poly.add a₁ x₁ p₁) p₂) (Lean.Grind.Linarith.Poly.combine._unary._proof_3 a₁ x₁ p₁ a₂ x₂ p₂)))))) _x))) (PSigma.rec (fun fst snd ↦ Lean.Grind.Linarith.Poly.combine.match_1.{1} (fun p₁ p₁ ↦ Lean.Grind.Linarith.Poly) fst snd (fun p₂ ↦ p₂) (fun p₂ ↦ p₂) fun a₁ x₁ p₁ a₂ x₂ p₂ ↦ cond (Nat.beq x₁ x₂) (cond (BEq.beq (HAdd.hAdd a₁ a₂) (OfNat.ofNat 0)) (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk p₁ p₂)) (Lean.Grind.Linarith.Poly.add (HAdd.hAdd a₁ a₂) x₁ (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk p₁ p₂)))) (cond (Nat.blt x₂ x₁) (Lean.Grind.Linarith.Poly.add a₁ x₁ (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk p₁ (Lean.Grind.Linarith.Poly.add a₂ x₂ p₂)))) (Lean.Grind.Linarith.Poly.add a₂ x₂ (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk (Lean.Grind.Linarith.Poly.add a₁ x₁ p₁) p₂))))) _x))) (Eq.refl (PSigma.rec (fun fst snd ↦ Lean.Grind.Linarith.Poly.combine.match_1.{1} (fun p₁ p₁ ↦ Lean.Grind.Linarith.Poly) fst snd (fun p₂ ↦ p₂) (fun p₂ ↦ p₂) fun a₁ x₁ p₁ a₂ x₂ p₂ ↦ cond (Nat.beq x₁ x₂) (cond (BEq.beq (HAdd.hAdd a₁ a₂) (OfNat.ofNat 0)) (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk p₁ p₂)) (Lean.Grind.Linarith.Poly.add (HAdd.hAdd a₁ a₂) x₁ (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk p₁ p₂)))) (cond (Nat.blt x₂ x₁) (Lean.Grind.Linarith.Poly.add a₁ x₁ (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk p₁ (Lean.Grind.Linarith.Poly.add a₂ x₂ p₂)))) (Lean.Grind.Linarith.Poly.add a₂ x₂ (Lean.Grind.Linarith.Poly.combine._unary (PSigma.mk (Lean.Grind.Linarith.Poly.add a₁ x₁ p₁) p₂))))) _x))))
has type
  (k : Int) → (v : Lean.Grind.Linarith.Var) → (p : Lean.Grind.Linarith.Poly) → (fun x ↦ (fun p₁ p₂ ↦ ((y : PSigma fun p₁ ↦ Lean.Grind.Linarith.Poly) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun p₁ p₂ ↦ HAdd.hAdd (SizeOf.sizeOf p₁) (SizeOf.sizeOf p₂)) y (PSigma.mk p₁ p₂) → Lean.Grind.Linarith.Poly) → Lean.Grind.Linarith.Poly) (Lean.Grind.Linarith.Poly.add k v p) x) p → ((y : PSigma fun p₁ ↦ Lean.Grind.Linarith.Poly) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun p₁ p₂ ↦ HAdd.hAdd (SizeOf.sizeOf p₁) (SizeOf.sizeOf p₂)) y (PSigma.mk (Lean.Grind.Linarith.Poly.add k v p) (Lean.Grind.Linarith.Poly.add k v p)) → Lean.Grind.Linarith.Poly) → Lean.Grind.Linarith.Poly
but is expected to have type
  (k : Int) → (v : Lean.Grind.Linarith.Var) → (p : Lean.Grind.Linarith.Poly) → (fun x ↦ (fun p₁ p₂ ↦ ((y : PSigma fun p₁ ↦ Lean.Grind.Linarith.Poly) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun p₁ p₂ ↦ HAdd.hAdd (SizeOf.sizeOf p₁) (SizeOf.sizeOf p₂)) y (PSigma.mk p₁ p₂) → Lean.Grind.Linarith.Poly) → Lean.Grind.Linarith.Poly) (Lean.Grind.Linarith.Poly.add k v p) x) p → (fun x ↦ (fun p₁ p₂ ↦ ((y : PSigma fun p₁ ↦ Lean.Grind.Linarith.Poly) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun p₁ p₂ ↦ HAdd.hAdd (SizeOf.sizeOf p₁) (SizeOf.sizeOf p₂)) y (PSigma.mk p₁ p₂) → Lean.Grind.Linarith.Poly) → Lean.Grind.Linarith.Poly) (Lean.Grind.Linarith.Poly.add k v p) x) (Lean.Grind.Linarith.Poly.add k v p)
theorem ENNReal.instLinearOrder._proof_2 : autoParam.{0} (∀ (a : ENNReal), ∀ (b : ENNReal), Eq (Min.min a b) (ite (LE.le a b) a b)) LinearOrder.min_def._autoParam := Lattice.toLinearOrder._proof_1 (WithTop.{0} NNReal)
has type
  (h : NNReal) → Decidable (LE.le (WithTop.some h) (WithTop.some h))
but is expected to have type
  (val : NNReal) → (fun x ↦ (fun x x ↦ Decidable (LE.le x x)) (Option.some h) x) (Option.some val)
theorem ENNReal.instLinearOrder._proof_3 : autoParam.{0} (∀ (a : ENNReal), ∀ (b : ENNReal), Eq (Max.max a b) (ite (LE.le a b) b a)) LinearOrder.max_def._autoParam := Lattice.toLinearOrder._proof_2 (WithTop.{0} NNReal)
has type
  (h : NNReal) → Decidable (LE.le (WithTop.some h) (WithTop.some h))
but is expected to have type
  (val : NNReal) → (fun x ↦ (fun x x ↦ Decidable (LE.le x x)) (Option.some h) x) (Option.some val)
theorem ENNReal.instLinearOrder._proof_4 : autoParam.{0} (∀ (a : ENNReal), ∀ (b : ENNReal), Eq (Ord.compare a b) (compareOfLessAndEq a b)) LinearOrder.compare_eq_compareOfLessAndEq._autoParam := Lattice.toLinearOrder._proof_3 (WithTop.{0} NNReal)
has type
  (h : NNReal) → (fun x ↦ Decidable (Eq (Option.some h) (Option.some h))) ((fun a b ↦ LinearOrder.toDecidableEq a b) h h)
but is expected to have type
  (val : NNReal) → (fun x ↦ (fun b ↦ Decidable (Eq (Option.some h) b)) x) (Option.some val)
theorem Std.DTreeMap.Internal.Impl.balanced_glue.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ {l : Std.DTreeMap.Internal.Impl β}, ∀ {r : Std.DTreeMap.Internal.Impl β}, ∀ {hl : Std.DTreeMap.Internal.Impl.Balanced l}, ∀ {hr : Std.DTreeMap.Internal.Impl.Balanced r}, ∀ {hlr : Std.DTreeMap.Internal.Impl.BalancedAtRoot (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)}, Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.glue l r hl hr hlr) := fun {α β l r hl hr hlr} ↦ Eq.mpr (id (congrArg (Std.DTreeMap.Internal.Impl.Balanced) (congrArg (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl β) l hl hlr fun hl hlr ↦ r) (funext fun sz ↦ funext fun k ↦ funext fun v ↦ funext fun l' ↦ funext fun r' ↦ funext fun hl ↦ funext fun hlr ↦ congrArg (Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl β) r hr hlr fun hr hlr ↦ l) (funext fun sz' ↦ funext fun k' ↦ funext fun v' ↦ funext fun l'' ↦ funext fun r'' ↦ funext fun hr ↦ funext fun hlr ↦ ite_congr (Eq.refl (LT.lt sz sz')) (fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)))) fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)))))))) (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.minView.match_3.splitter r (fun l hl hlr ↦ Eq l l → HEq hl hl → HEq hlr hlr → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl β) l hl hlr (fun hl hlr ↦ r) fun sz k v l' r' hl hlr ↦ Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl β) r hr hlr (fun hr hlr ↦ l) fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt sz sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))))) l hl hlr (fun hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id hr) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (fun size k' v' l' r' hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.glue.match_1.splitter size k' v' l' r' (fun r hr hlr ↦ Eq r r → HEq hr hr → HEq hlr hlr → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.glue.match_1 size k' v' l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl β) r hr hlr (fun hr hlr ↦ Std.DTreeMap.Internal.Impl.inner size k' v' l' r') fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt size sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner size k' v' l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))))) r hr hlr (fun hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (Eq.mpr (id (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1)) (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ And.intro left (And.intro left (And.intro left right))) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (fun sz' k' v' l'' r'' hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (Decidable.casesOn (Nat.decLt size sz') (fun h ↦ Eq.mpr (id (congrArg (Std.DTreeMap.Internal.Impl.Balanced) (if_neg h))) (of_eq_true (Std.DTreeMap.Internal.Impl.balanced_balanceRErase._simp_1 (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))))) fun h ↦ Eq.mpr (id (congrArg (Std.DTreeMap.Internal.Impl.Balanced) (if_pos h))) (of_eq_true (Std.DTreeMap.Internal.Impl.balanced_balanceLErase._simp_1 hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (Eq.refl r) (HEq.refl hr) (HEq.refl hlr))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (Eq.refl l) (HEq.refl hl) (HEq.refl hlr))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r' hlb hlr) r → (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) (Std.DTreeMap.Internal.Impl.inner size k v l r) r' hlb hlr
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r' hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r' hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.size_glue.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ {l : Std.DTreeMap.Internal.Impl β}, ∀ {r : Std.DTreeMap.Internal.Impl β}, ∀ {hl : Std.DTreeMap.Internal.Impl.Balanced l}, ∀ {hr : Std.DTreeMap.Internal.Impl.Balanced r}, ∀ {hlr : Std.DTreeMap.Internal.Impl.BalancedAtRoot (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)}, Eq (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.glue l r hl hr hlr)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)) := fun {α β l r hl hr hlr} ↦ Eq.mpr (id (congrFun' (congrArg (Eq) (congrArg (Std.DTreeMap.Internal.Impl.size) (congrArg (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl β) l hl hlr fun hl hlr ↦ r) (funext fun sz ↦ funext fun k ↦ funext fun v ↦ funext fun l' ↦ funext fun r' ↦ funext fun hl ↦ funext fun hlr ↦ congrArg (Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl β) r hr hlr fun hr hlr ↦ l) (funext fun sz' ↦ funext fun k' ↦ funext fun v' ↦ funext fun l'' ↦ funext fun r'' ↦ funext fun hr ↦ funext fun hlr ↦ ite_congr (Eq.refl (LT.lt sz sz')) (fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)))) fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)))))))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)))) (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.minView.match_3.splitter r (fun l hl hlr ↦ Eq l l → HEq hl hl → HEq hlr hlr → Eq (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl β) l hl hlr (fun hl hlr ↦ r) fun sz k v l' r' hl hlr ↦ Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl β) r hr hlr (fun hr hlr ↦ l) fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt sz sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r))) l hl hlr (fun hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (id (Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.minView._proof_5 r a))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (fun size k' v' l' r' hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.glue.match_1.splitter size k' v' l' r' (fun r hr hlr ↦ Eq r r → HEq hr hr → HEq hlr hlr → Eq (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.glue.match_1 size k' v' l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl β) r hr hlr (fun hr hlr ↦ Std.DTreeMap.Internal.Impl.inner size k' v' l' r') fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt size sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner size k' v' l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k' v' l' r')) (Std.DTreeMap.Internal.Impl.size r))) r hr hlr (fun hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (id (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr hlr right h ↦ Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.size_glue._proof_1_9 l' r' a) h hlr hlr right) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r'))) (HEq.refl right)) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (fun sz' k' v' l'' r'' hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (Decidable.casesOn (Nat.decLt size sz') (fun h ↦ Eq.mpr (id (congrFun' (congrArg (Eq) (congrArg (Std.DTreeMap.Internal.Impl.size) (if_neg h))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k' v' l' r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r''))))) (Eq.mpr (id (congrFun' (congrArg (Eq) (Eq.trans (Std.DTreeMap.Internal.Impl.size_balanceRErase (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (congrFun' (congrArg (HAdd.hAdd) (congrFun' (congrArg (HAdd.hAdd) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (OfNat.ofNat 1))) sz'))) (HAdd.hAdd size sz'))) (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr hlr h right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr right hlr h h ↦ Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.size_glue._proof_1_11 l' r' l'' r'' a) h hlr right hlr h) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r'))) (HEq.refl right)) h hlr hlr h right) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l'') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r''))) (HEq.refl right)) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr))))) fun h ↦ Eq.mpr (id (congrFun' (congrArg (Eq) (congrArg (Std.DTreeMap.Internal.Impl.size) (if_pos h))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k' v' l' r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r''))))) (Eq.mpr (id (congrFun' (congrArg (Eq) (Eq.trans (Std.DTreeMap.Internal.Impl.size_balanceLErase hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (congrArg (HAdd.hAdd (HAdd.hAdd size (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)))) (HAdd.hAdd size sz'))) (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr hlr h right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr right hlr h h ↦ Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.size_glue._proof_1_10 l' r' l'' r'' a) h hlr right hlr h) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r'))) (HEq.refl right)) h hlr hlr h right) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l'') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r''))) (HEq.refl right)) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr)))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (Eq.refl r) (HEq.refl hr) (HEq.refl hlr))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (Eq.refl l) (HEq.refl hl) (HEq.refl hlr))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r' hlb hlr) r → (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) (Std.DTreeMap.Internal.Impl.inner size k v l r) r' hlb hlr
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r' hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r' hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.toListModel_minView.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ {k : α}, ∀ {v : β k}, ∀ {l : Std.DTreeMap.Internal.Impl β}, ∀ {r : Std.DTreeMap.Internal.Impl β}, ∀ {hl : Std.DTreeMap.Internal.Impl.Balanced l}, ∀ {hr : Std.DTreeMap.Internal.Impl.Balanced r}, ∀ {hlr : Std.DTreeMap.Internal.Impl.BalancedAtRoot (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)}, Eq (List.cons (Sigma.mk (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr)) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr))) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.View.tree (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr))))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))) := fun {α β k v l r hl hr hlr} ↦ Std.DTreeMap.Internal.Impl.minView.induct (fun {k v l r hl hr hlr} ↦ Eq (List.cons (Sigma.mk (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr)) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr))) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.View.tree (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr))))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (fun k v r hr hl hlr ↦ of_eq_true (eq_self (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (fun k v r hr size k' v' l' r' hl hlr dk dv dt hdt hdt' x ih1 ↦ of_eq_true (Eq.trans (congr (congrArg (Eq) (congrArg (List.cons (Sigma.mk (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l' r' (Std.DTreeMap.Internal.Impl.minView._proof_9 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_11 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_13 size k' v' l' r' hl))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l' r' (Std.DTreeMap.Internal.Impl.minView._proof_9 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_11 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_13 size k' v' l' r' hl))))) (Std.DTreeMap.Internal.Impl.toListModel_balanceRErase))) (congrFun' (congrArg (HAppend.hAppend) (Eq.symm ih1)) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (eq_self (List.cons (Sigma.mk (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l' r' (Std.DTreeMap.Internal.Impl.minView._proof_9 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_11 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_13 size k' v' l' r' hl))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l' r' (Std.DTreeMap.Internal.Impl.minView._proof_9 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_11 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_13 size k' v' l' r' hl)))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l' r' (Std.DTreeMap.Internal.Impl.minView._proof_9 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_11 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_13 size k' v' l' r' hl)).tree)) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))))) k v l r hl hr hlr
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) → Std.DTreeMap.Internal.Impl β
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.toListModel_glue.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ {l : Std.DTreeMap.Internal.Impl β}, ∀ {r : Std.DTreeMap.Internal.Impl β}, ∀ {hl : Std.DTreeMap.Internal.Impl.Balanced l}, ∀ {hr : Std.DTreeMap.Internal.Impl.Balanced r}, ∀ {hlr : Std.DTreeMap.Internal.Impl.BalancedAtRoot (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)}, Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.glue l r hl hr hlr)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (Std.DTreeMap.Internal.Impl.toListModel r)) := fun {α β l r hl hr hlr} ↦ Std.DTreeMap.Internal.Impl.casesOn l (fun size k v l r h ↦ Eq.ndrec (fun {hl hlr} ↦ Std.DTreeMap.Internal.Impl.casesOn r (fun size k v l r h ↦ Eq.ndrec (fun {hr hlr} ↦ id (Decidable.casesOn (Nat.decLt size size) (fun h ↦ Eq.mpr (id (congrFun' (congrArg (Eq) (congrArg (Std.DTreeMap.Internal.Impl.toListModel) (if_neg h))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r))))) (Eq.mpr (id (congrArg (fun _a ↦ Eq _a (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)))) (Std.DTreeMap.Internal.Impl.toListModel_balanceRErase))) (Eq.mpr (id (congrArg (fun _a ↦ Eq (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l r (Std.DTreeMap.Internal.Impl.glue._proof_14 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k v l r hl size k v l r hr)).tree)) _a) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)))) (Eq.symm (List.singleton_append)))) (Eq.mpr (id (congrArg (fun _a ↦ Eq _a (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)))) (Eq.symm (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l r (Std.DTreeMap.Internal.Impl.glue._proof_14 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k v l r hl size k v l r hr)).tree)) (List.cons (Sigma.mk (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l r (Std.DTreeMap.Internal.Impl.glue._proof_14 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k v l r hl size k v l r hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l r (Std.DTreeMap.Internal.Impl.glue._proof_14 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k v l r hl size k v l r hr)))) (List.nil)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)))))) (of_eq_true (Eq.trans (congr (congrArg (Eq) (Eq.trans (congrFun' (congrArg (HAppend.hAppend) (Std.DTreeMap.Internal.Impl.toListModel_maxView)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))))) (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (eq_self (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel r) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))))))))))) fun h ↦ Eq.mpr (id (congrFun' (congrArg (Eq) (congrArg (Std.DTreeMap.Internal.Impl.toListModel) (if_pos h))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r))))) (of_eq_true (Eq.trans (congr (congrArg (Eq) (Eq.trans (Std.DTreeMap.Internal.Impl.toListModel_balanceLErase) (Eq.trans (congrArg (HAppend.hAppend (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (Std.DTreeMap.Internal.Impl.toListModel_minView)) (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))))) (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (eq_self (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel r) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))))))))) (Eq.symm h) hr hlr) (fun h ↦ Eq.ndrec (fun {hr hlr} ↦ of_eq_true (Eq.trans (congrArg (Eq (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (List.append_nil (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (eq_self (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))))) (Eq.symm h) hr hlr) (Eq.refl r)) (Eq.symm h) hl hlr) (fun h ↦ Eq.ndrec (fun {hl hlr} ↦ Std.DTreeMap.Internal.Impl.casesOn r (fun size k v l r h ↦ Eq.ndrec (fun {hr hlr} ↦ of_eq_true (eq_self (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (Eq.symm h) hr hlr) (fun h ↦ Eq.ndrec (fun {hr hlr} ↦ of_eq_true (Eq.trans (congrArg (Eq (List.nil)) (List.append_nil (List.nil))) (eq_self (List.nil)))) (Eq.symm h) hr hlr) (Eq.refl r)) (Eq.symm h) hl hlr) (Eq.refl l)
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v x r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v x r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r hlb hlr) r → (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) (Std.DTreeMap.Internal.Impl.inner size k v l r) r hlb hlr
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v x r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v x r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v x r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x r hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.alter_eq_alterₘ.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ [inst : Ord.{u} α], ∀ [inst : Std.TransOrd α], ∀ [inst : Std.LawfulEqOrd α], ∀ {t : Std.DTreeMap.Internal.Impl β}, ∀ {a : α}, ∀ {f : Option.{v} (β a) → Option.{v} (β a)}, ∀ (htb : Std.DTreeMap.Internal.Impl.Balanced t), Std.DTreeMap.Internal.Impl.Ordered t → Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f t htb)) (Std.DTreeMap.Internal.Impl.alterₘ a f t htb) := fun {α β} [inst : Ord.{u} #1] [inst : Std.TransOrd #2] [inst : Std.LawfulEqOrd #3] {t a f} htb hto ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f t htb)) _a) (Std.DTreeMap.Internal.Impl.alterₘ.eq_1 a f t htb))) (Std.DTreeMap.Internal.Impl.rec (fun sz k v l r ihl ihr htb hto ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) (Std.DTreeMap.Internal.Impl.inner sz k v l r) htb))) (Std.DTreeMap.Internal.Impl.alter.eq_2 a f sz k v l r htb))) (Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_13 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_15 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_18 sz k v l r htb d hd hd'₁ hd'₂)) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_20 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_22 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_25 sz k v l r htb d hd hd'₁ hd'₂)) fun h ↦ Std.DTreeMap.Internal.Impl.«getThenInsertIfNew?».match_1 a (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k h) v))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_13 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.erase._proof_34 sz k v l r htb) (Std.DTreeMap.Internal.Impl.erase._proof_36 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_28 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.alter._proof_30 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_33 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_35 a sz k v l r htb v))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a)) (Std.DTreeMap.Internal.Impl.updateCell.eq_2 a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) sz k v l r htb))) (_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.alter.match_3.splitter.{0} (fun x ↦ Eq (Ord.compare a k) x → Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_13 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_15 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_18 sz k v l r htb d hd hd'₁ hd'₂)) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_20 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_22 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_25 sz k v l r htb d hd hd'₁ hd'₂)) fun h ↦ Std.DTreeMap.Internal.Impl.«getThenInsertIfNew?».match_1 a (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans (Eq.refl (Ord.compare a k)) h)) v))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_13 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.erase._proof_34 sz k v l r htb) (Std.DTreeMap.Internal.Impl.erase._proof_36 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_28 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.alter._proof_30 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_33 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_35 a sz k v l r htb v))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_3 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)) fun newL h₁ h₂ h₃ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v newL r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb newL h₁) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb newL h₂ h₃)) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb newL h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb newL h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb newL h₁ h₂ h₃)) (fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')) fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_3 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)) fun newR h₁ h₂ h₃ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l newR (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb newR h₁) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb newR h₂ h₃)) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb newR h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb newR h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb newR h₁ h₂ h₃)))) (Ord.compare a k) (fun h h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (of_eq_true (Eq.trans (congrFun' (congrArg (Eq) (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.Balanced.left htb))) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto)) r r (Eq.refl r) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))))) (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (eq_self (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.Balanced.left htb))) r (Eq.ndrec (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto))) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Eq.ndrec (Eq.ndrec (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (Eq.refl r)) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto))))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun h h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (of_eq_true (Eq.trans (congrFun' (congrArg (Eq) (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) l l (Eq.refl l) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto)) (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))))) (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))))) (eq_self (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Eq.ndrec (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto))) (Eq.ndrec (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto))))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun h h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.«getThenInsertIfNew?».match_1 a (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans heq (Eq.refl Ordering.eq))) v))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_13 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.erase._proof_34 sz k v l r htb) (Std.DTreeMap.Internal.Impl.erase._proof_36 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_28 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.alter._proof_30 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_33 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_35 a sz k v l r htb v)))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (Eq.symm (id (Option.casesOn (f (Option.some (Eq.rec v (Std.DTreeMap.Internal.Cell.alter._proof_1 (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq (Eq.refl Ordering.eq)) k v (Eq.refl (Option.some (Sigma.mk k v))))))) (fun h ↦ Eq.ndrec (fun h₁ ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.ofOption.match_1 a (fun «v?» ↦ Std.DTreeMap.Internal.Cell α β (Ord.compare a)) (Option.none) (fun _ ↦ Std.DTreeMap.Internal.Cell.empty) fun v ↦ Std.DTreeMap.Internal.Cell.of a v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')))) (Eq.symm h) (Eq.refl (f (Option.some (Eq.rec v (Std.DTreeMap.Internal.Cell.alter._proof_1 (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq (Eq.refl Ordering.eq)) k v (Eq.refl (Option.some (Sigma.mk k v))))))))) (fun val h ↦ Eq.ndrec (fun h₁ ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.ofOption.match_1 a (fun «v?» ↦ Std.DTreeMap.Internal.Cell α β (Ord.compare a)) (Option.some val) (fun _ ↦ Std.DTreeMap.Internal.Cell.empty) fun v ↦ Std.DTreeMap.Internal.Cell.of a v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')))) (Eq.symm h) (Eq.refl (f (Option.some (Eq.rec v (Std.DTreeMap.Internal.Cell.alter._proof_1 (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq (Eq.refl Ordering.eq)) k v (Eq.refl (Option.some (Sigma.mk k v))))))))) (Eq.refl (f (Option.some (Eq.rec v (Std.DTreeMap.Internal.Cell.alter._proof_1 (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq (Eq.refl Ordering.eq)) k v (Eq.refl (Option.some (Sigma.mk k v))))))))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (Eq.refl (Ord.compare a k))))) (fun htb hto ↦ id (Option.casesOn (f (Option.none)) (fun h ↦ Eq.ndrec (of_eq_true (eq_self (Std.DTreeMap.Internal.Impl.leaf))) (Eq.symm h)) (fun val h ↦ Eq.ndrec (of_eq_true (eq_self (Std.DTreeMap.Internal.Impl.inner (OfNat.ofNat 1) a val (Std.DTreeMap.Internal.Impl.leaf) (Std.DTreeMap.Internal.Impl.leaf)))) (Eq.symm h)) (Eq.refl (f (Option.none))))) t htb hto)
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl β) x hr h) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → Std.DTreeMap.Internal.Impl β
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl β) x hr h) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl β) x hr h) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.Const.alter_eq_alterₘ.{u, v} : ∀ {α : Type u}, ∀ {β : Type v}, ∀ [inst : Ord.{u} α], ∀ [inst : Std.TransOrd α], ∀ {t : Std.DTreeMap.Internal.Impl fun x ↦ β}, ∀ {a : α}, ∀ {f : Option.{v} β → Option.{v} β}, ∀ (htb : Std.DTreeMap.Internal.Impl.Balanced t), Std.DTreeMap.Internal.Impl.Ordered t → Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f t htb)) (Std.DTreeMap.Internal.Impl.Const.alterₘ a f t htb) := fun {α β} [inst : Ord.{u} #1] [inst : Std.TransOrd #2] {t a f} htb hto ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f t htb)) _a) (Std.DTreeMap.Internal.Impl.Const.alterₘ.eq_1 a f t htb))) (Std.DTreeMap.Internal.Impl.rec (fun sz k v l r ihl ihr htb hto ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) (Std.DTreeMap.Internal.Impl.inner sz k v l r) htb))) (Std.DTreeMap.Internal.Impl.Const.alter.eq_2 a f sz k v l r htb))) (Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_24 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_27 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_30 sz k v l r htb d hd hd'₁ hd'₂)) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_32 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_35 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_38 sz k v l r htb d hd hd'₁ hd'₂)) fun _ ↦ Std.DTreeMap.Internal.Impl.Const.«getThenInsertIfNew?».match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_40 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_42 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_45 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_48 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_50 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_53 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_56 a sz k v l r htb v))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a)) (Std.DTreeMap.Internal.Impl.updateCell.eq_2 a (Std.DTreeMap.Internal.Cell.Const.alter f) sz k v l r htb))) (_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.insert.match_3.splitter.{0} (fun x ↦ Eq (Ord.compare a k) x → Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_24 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_27 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_30 sz k v l r htb d hd hd'₁ hd'₂)) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_32 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_35 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_38 sz k v l r htb d hd hd'₁ hd'₂)) fun _ ↦ Std.DTreeMap.Internal.Impl.Const.«getThenInsertIfNew?».match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_40 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_42 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_45 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_48 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_50 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_53 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_56 a sz k v l r htb v))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_3 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)) fun newL h₁ h₂ h₃ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v newL r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb newL h₁) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb newL h₂ h₃)) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb newL h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb newL h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb newL h₁ h₂ h₃)) (fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.Const.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')) fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_3 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)) fun newR h₁ h₂ h₃ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l newR (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb newR h₁) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb newR h₂ h₃)) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb newR h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb newR h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb newR h₁ h₂ h₃)))) (Ord.compare a k) (fun a h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.Const.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (of_eq_true (Eq.trans (congrFun' (congrArg (Eq) (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.Balanced.left htb))) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto)) r r (Eq.refl r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))))) (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (eq_self (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.Balanced.left htb))) r (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Eq.ndrec (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (Eq.refl r)) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto))))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun a h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.Const.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (of_eq_true (Eq.trans (congrFun' (congrArg (Eq) (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) l l (Eq.refl l) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))))) (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))))) (eq_self (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto))) (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto))))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun a h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.«getThenInsertIfNew?».match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_40 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_42 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_45 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_48 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_50 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_53 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_56 a sz k v l r htb v)))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.Const.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (Eq.symm (id (Option.casesOn (f (Option.some v)) (fun h ↦ Eq.ndrec (fun h₁ ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.ofOption.match_1 a (fun «v?» ↦ Std.DTreeMap.Internal.Cell α (fun x ↦ β) (Ord.compare a)) (Option.none) (fun _ ↦ Std.DTreeMap.Internal.Cell.empty) fun v ↦ Std.DTreeMap.Internal.Cell.of a v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')))) (Eq.symm h) (Eq.refl (f (Option.some v)))) (fun val h ↦ Eq.ndrec (fun h₁ ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.ofOption.match_1 a (fun «v?» ↦ Std.DTreeMap.Internal.Cell α (fun x ↦ β) (Ord.compare a)) (Option.some val) (fun _ ↦ Std.DTreeMap.Internal.Cell.empty) fun v ↦ Std.DTreeMap.Internal.Cell.of a v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')))) (Eq.symm h) (Eq.refl (f (Option.some v)))) (Eq.refl (f (Option.some v)))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (Eq.refl (Ord.compare a k))))) (fun htb hto ↦ id (Option.casesOn (f (Option.none)) (fun h ↦ Eq.ndrec (of_eq_true (eq_self (Std.DTreeMap.Internal.Impl.leaf))) (Eq.symm h)) (fun val h ↦ Eq.ndrec (of_eq_true (eq_self (Std.DTreeMap.Internal.Impl.inner (OfNat.ofNat 1) a val (Std.DTreeMap.Internal.Impl.leaf) (Std.DTreeMap.Internal.Impl.leaf)))) (Eq.symm h)) (Eq.refl (f (Option.none))))) t htb hto)
has type
  (size : Nat) → (k : α) → (v : (fun x ↦ β) k) → (l : Std.DTreeMap.Internal.Impl fun x ↦ β) → (r : Std.DTreeMap.Internal.Impl fun x ↦ β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) x hr h) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → Std.DTreeMap.Internal.Impl fun x ↦ β
but is expected to have type
  (size : Nat) → (k : α) → (v : (fun x ↦ β) k) → (l : Std.DTreeMap.Internal.Impl fun x ↦ β) → (r : Std.DTreeMap.Internal.Impl fun x ↦ β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) x hr h) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) x hr h) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.modify_eq_alter.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ [inst : Ord.{u} α], ∀ [inst : Std.LawfulEqOrd α], ∀ {t : Std.DTreeMap.Internal.Impl β}, ∀ {a : α}, ∀ {f : β a → β a}, ∀ (htb : Std.DTreeMap.Internal.Impl.Balanced t), Eq (Std.DTreeMap.Internal.Impl.modify a f t) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) t htb)) := fun {α β} [inst : Ord.{u} #1] [inst : Std.LawfulEqOrd #2] {t a f} htb ↦ Std.DTreeMap.Internal.Impl.rec (fun sz k v l r ihl ihr htb ↦ let hmb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.modify a f (Std.DTreeMap.Internal.Impl.inner sz k v l r)) := Std.DTreeMap.Internal.Impl.balanced_modify htb
Eq.mpr (id (congrArg (fun _a ↦ Eq _a (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) (Std.DTreeMap.Internal.Impl.inner sz k v l r) htb))) (Std.DTreeMap.Internal.Impl.modify.eq_2 a f sz k v l r))) (Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl β) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.modify a f l) r) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.modify a f r)) fun h ↦ Std.DTreeMap.Internal.Impl.inner sz a (f (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k h) v)) l r) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a)) (Std.DTreeMap.Internal.Impl.alter.eq_2 a (fun x ↦ Option.map f x) sz k v l r htb))) (_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.alter.match_3.splitter.{0} (fun x ↦ Eq (Ord.compare a k) x → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl β) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.modify a f l) r) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.modify a f r)) fun h ↦ Std.DTreeMap.Internal.Impl.inner sz a (f (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans (Eq.refl (Ord.compare a k)) h)) v)) l r) → Eq (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl β) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.modify a f l) r) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.modify a f r)) fun h ↦ Std.DTreeMap.Internal.Impl.inner sz a (f (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans (Eq.refl (Ord.compare a k)) h)) v)) l r) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_13 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_15 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_18 sz k v l r htb d hd hd'₁ hd'₂)) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_20 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_22 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_25 sz k v l r htb d hd hd'₁ hd'₂)) fun h ↦ Std.DTreeMap.Internal.Impl.«getThenInsertIfNew?».match_1 a (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Option.map f (Option.some (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans (Eq.refl (Ord.compare a k)) h)) v))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_13 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.erase._proof_34 sz k v l r htb) (Std.DTreeMap.Internal.Impl.erase._proof_36 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_28 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.alter._proof_30 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_33 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_35 a sz k v l r htb v)))) (Ord.compare a k) (fun h h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ of_eq_true (Eq.trans (congrArg (Eq (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.modify a f l) r)) (Eq.trans (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.modify a f l) (Eq.symm (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb))) r r (Eq.refl r) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))))) ((fun x_0 ↦ (fun x_0 ↦ Std.DTreeMap.Internal.Impl.balance_eq_inner hmb) x_0) (Eq.ndrec (Eq.ndrec (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (Eq.refl r)) (Eq.symm (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb))))))) (eq_self (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.modify a f l) r)))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun h h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ of_eq_true (Eq.trans (congrArg (Eq (Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.modify a f r))) (Eq.trans (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) l l (Eq.refl l) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.modify a f r) (Eq.symm (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))))) ((fun x_0 ↦ (fun x_0 ↦ Std.DTreeMap.Internal.Impl.balance_eq_inner hmb) x_0) (Eq.ndrec (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (Eq.symm (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb))))))) (eq_self (Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.modify a f r))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun h h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ Eq.refl (Std.DTreeMap.Internal.Impl.inner sz a (f (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans heq (Eq.refl Ordering.eq))) v)) l r)) (Eq.symm h) (Eq.refl (Ord.compare a k))) (Eq.refl (Ord.compare a k)) (Eq.mp (congrArg (fun l ↦ Std.DTreeMap.Internal.Impl.Balanced l) (Std.DTreeMap.Internal.Impl.modify.eq_2 a f sz k v l r)) hmb)))) (fun htb ↦ Eq.refl (Std.DTreeMap.Internal.Impl.modify a f (Std.DTreeMap.Internal.Impl.leaf))) t htb
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl β) x hr h) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → Std.DTreeMap.Internal.Impl β
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl β) x hr h) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl β) x hr h) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.Const.modify_eq_alter.{u, v} : ∀ {α : Type u}, ∀ {β : Type v}, ∀ [inst : Ord.{u} α], [Std.TransOrd α] → ∀ {t : Std.DTreeMap.Internal.Impl fun x ↦ β}, ∀ {a : α}, ∀ {f : β → β}, ∀ (htb : Std.DTreeMap.Internal.Impl.Balanced t), Eq (Std.DTreeMap.Internal.Impl.Const.modify a f t) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) t htb)) := fun {α β} [inst : Ord.{u} #1] [inst : Std.TransOrd #2] {t a f} htb ↦ Std.DTreeMap.Internal.Impl.rec (fun sz k v l r ihl ihr htb ↦ let hmb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.Const.modify a f (Std.DTreeMap.Internal.Impl.inner sz k v l r)) := Std.DTreeMap.Internal.Impl.Const.balanced_modify htb
Eq.mpr (id (congrArg (fun _a ↦ Eq _a (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) (Std.DTreeMap.Internal.Impl.inner sz k v l r) htb))) (Std.DTreeMap.Internal.Impl.Const.modify.eq_2 a f sz k v l r))) (Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.Const.modify a f l) r) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.Const.modify a f r)) fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz a (f v) l r) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a)) (Std.DTreeMap.Internal.Impl.Const.alter.eq_2 a (fun x ↦ Option.map f x) sz k v l r htb))) (_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.insert.match_3.splitter.{0} (fun x ↦ Eq (Ord.compare a k) x → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.Const.modify a f l) r) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.Const.modify a f r)) fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz a (f v) l r) → Eq (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.Const.modify a f l) r) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.Const.modify a f r)) fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz a (f v) l r) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_24 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_27 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_30 sz k v l r htb d hd hd'₁ hd'₂)) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_32 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_35 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_38 sz k v l r htb d hd hd'₁ hd'₂)) fun _ ↦ Std.DTreeMap.Internal.Impl.Const.«getThenInsertIfNew?».match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Option.map f (Option.some v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_40 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_42 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_45 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_48 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_50 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_53 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_56 a sz k v l r htb v)))) (Ord.compare a k) (fun a h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ id (of_eq_true (Eq.trans (congrArg (Eq (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.Const.modify a f l) r)) (Eq.trans (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.Const.modify a f l) (Eq.symm (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb))) r r (Eq.refl r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))))) ((fun x_0 ↦ (fun x_0 ↦ Std.DTreeMap.Internal.Impl.balance_eq_inner hmb) x_0) (Eq.ndrec (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (Eq.refl r)) (Eq.symm (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb))))))) (eq_self (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.Const.modify a f l) r))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun a h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ id (of_eq_true (Eq.trans (congrArg (Eq (Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.Const.modify a f r))) (Eq.trans (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) l l (Eq.refl l) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.Const.modify a f r) (Eq.symm (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))))) ((fun x_0 ↦ (fun x_0 ↦ Std.DTreeMap.Internal.Impl.balance_eq_inner hmb) x_0) (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (Eq.symm (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb))))))) (eq_self (Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.Const.modify a f r)))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun a h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ Eq.refl (Std.DTreeMap.Internal.Impl.inner sz a (f v) l r)) (Eq.symm h) (Eq.refl (Ord.compare a k))) (Eq.refl (Ord.compare a k)) (Eq.mp (congrArg (fun _a ↦ Std.DTreeMap.Internal.Impl.Balanced _a) (Std.DTreeMap.Internal.Impl.Const.modify.eq_2 a f sz k v l r)) hmb)))) (fun htb ↦ Eq.refl (Std.DTreeMap.Internal.Impl.Const.modify a f (Std.DTreeMap.Internal.Impl.leaf))) t htb
has type
  (size : Nat) → (k : α) → (v : (fun x ↦ β) k) → (l : Std.DTreeMap.Internal.Impl fun x ↦ β) → (r : Std.DTreeMap.Internal.Impl fun x ↦ β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) x hr h) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → Std.DTreeMap.Internal.Impl fun x ↦ β
but is expected to have type
  (size : Nat) → (k : α) → (v : (fun x ↦ β) k) → (l : Std.DTreeMap.Internal.Impl fun x ↦ β) → (r : Std.DTreeMap.Internal.Impl fun x ↦ β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) x hr h) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl fun x ↦ β) x hr h) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.link._unary.eq_def.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ (k : α), ∀ (v : β k), ∀ (_x : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r), Eq (Std.DTreeMap.Internal.Impl.link._unary k v _x) (PSigma.casesOn _x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) l hl (fun hl ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size r)) := Std.DTreeMap.Internal.Impl.insertMin k v r (Std.DTreeMap.Internal.Impl.link._proof_6 r hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v r hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v r hr)) fun szl k' v' l' r' hl ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) r hr (fun hr ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) fun szr k'' v'' l'' r'' hr ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._proof_39 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._proof_41 k v szl k' v' l' r' szr k'' v'' l'' r'')) := fun {α β} k v _x ↦ id (Eq.trans (WellFounded.Nat.fix_eq (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) (fun _x a ↦ PSigma.casesOn _x (fun l r a ↦ PSigma.casesOn r (fun r hl a ↦ PSigma.casesOn hl (fun hl hr a ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk l (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) l hl (fun hl x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size r)) := Std.DTreeMap.Internal.Impl.insertMin k v r (Std.DTreeMap.Internal.Impl.link._proof_6 r hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v r hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v r hr)) (fun szl k' v' l' r' hl x ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) r hr (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) (fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v szl k' v' l' r' szr k'' v'' l'' r'')) x) a) a) a) a) _x) (Eq.mpr (id (congrFun' (congrArg (Eq) (Eq.trans (_private.Std.Data.DTreeMap.Internal.Operations.0.PSigma.casesOn._arg_pusher (PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) (fun _x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size _x.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size _x.snd.fst))) (Std.DTreeMap.Internal.Impl.link._unary k v) (fun _x y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y _x) _x fun l r a ↦ PSigma.casesOn r (fun r hl a ↦ PSigma.casesOn hl (fun hl hr a ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk l (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) l hl (fun hl x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size r)) := Std.DTreeMap.Internal.Impl.insertMin k v r (Std.DTreeMap.Internal.Impl.link._proof_6 r hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v r hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v r hr)) (fun szl k' v' l' r' hl x ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) r hr (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) (fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v szl k' v' l' r' szr k'' v'' l'' r'')) x) a) a) a) (congrFun (congrArg (PSigma.rec) (funext fun fst ↦ funext fun snd ↦ Eq.trans (_private.Std.Data.DTreeMap.Internal.Operations.0.PSigma.casesOn._arg_pusher (PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) (fun _x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size _x.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size _x.snd.fst))) (Std.DTreeMap.Internal.Impl.link._unary k v) (fun r y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk fst r)) snd fun r hl a ↦ PSigma.casesOn hl (fun hl hr a ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk l (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) fst hl (fun hl x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size r)) := Std.DTreeMap.Internal.Impl.insertMin k v r (Std.DTreeMap.Internal.Impl.link._proof_6 r hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v r hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v r hr)) (fun szl k' v' l' r' hl x ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) r hr (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) (fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v szl k' v' l' r' szr k'' v'' l'' r'')) x) a) a) (congrFun (congrArg (PSigma.rec) (funext fun fst ↦ funext fun snd ↦ Eq.trans (_private.Std.Data.DTreeMap.Internal.Operations.0.PSigma.casesOn._arg_pusher (PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) (fun _x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size _x.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size _x.snd.fst))) (Std.DTreeMap.Internal.Impl.link._unary k v) (fun hl y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk fst (PSigma.mk fst hl))) snd fun hl hr a ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk l (PSigma.mk fst (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size fst))) fst hl (fun hl x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size fst)) := Std.DTreeMap.Internal.Impl.insertMin k v fst (Std.DTreeMap.Internal.Impl.link._proof_6 fst hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v fst hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v fst hr)) (fun szl k' v' l' r' hl x ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) fst hr (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) (fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v szl k' v' l' r' szr k'' v'' l'' r'')) x) a) (congrFun (congrArg (PSigma.rec) (funext fun fst ↦ funext fun snd ↦ Eq.trans (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.insertMin.match_3._arg_pusher (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size fst))) (PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) (fun _x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size _x.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size _x.snd.fst))) (Std.DTreeMap.Internal.Impl.link._unary k v) (fun l hl y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk l (PSigma.mk fst (PSigma.mk hl snd)))) fst fst (fun hl x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size fst)) := Std.DTreeMap.Internal.Impl.insertMin k v fst (Std.DTreeMap.Internal.Impl.link._proof_6 fst snd)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v fst snd) (Std.DTreeMap.Internal.Impl.link._proof_10 k v fst snd)) fun szl k' v' l' r' hl x ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) fst snd (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) (fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v szl k' v' l' r' szr k'' v'' l'' r'')) x) (congrArg (Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size fst))) fst fst fun hr ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v fst (Std.DTreeMap.Internal.Impl.link._proof_6 fst snd))) (Std.DTreeMap.Internal.Impl.link._proof_8 k v fst snd) (Std.DTreeMap.Internal.Impl.link._proof_10 k v fst snd)) (funext fun sz ↦ funext fun k' ↦ funext fun v' ↦ funext fun l' ↦ funext fun r' ↦ funext fun hr ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.insertMin.match_3._arg_pusher (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) (PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) (fun _x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size _x.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size _x.snd.fst))) (Std.DTreeMap.Internal.Impl.link._unary k v) (fun r hr y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (PSigma.mk r (PSigma.mk hr hr)))) fst snd (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 sz k' v' l' r' hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.link._proof_16 k v sz k' v' l' r' hr)) fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta sz) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 sz k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 sz k' v' l' r' hr szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k' v' l' r' hr szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k' v' l' r' hr szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k' v' l' r' hr szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) sz) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k' v' l' r' hr szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 sz k' v' l' r' hr szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k' v' l' r' hr szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k' v' l' r' hr szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd sz (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v sz k' v' l' r' szr k'' v'' l'' r''))))) snd))) snd))) _x))) (PSigma.rec (fun fst snd ↦ PSigma.rec (fun fst snd ↦ PSigma.rec (fun fst snd ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size fst))) fst fst (fun hr ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v fst (Std.DTreeMap.Internal.Impl.link._proof_6 fst snd))) (Std.DTreeMap.Internal.Impl.link._proof_8 k v fst snd) (Std.DTreeMap.Internal.Impl.link._proof_10 k v fst snd)) fun szl k' v' l' r' hl ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) fst snd (fun hr ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl))) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) fun szr k'' v'' l'' r'' hr ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Eq.ndrec (Std.DTreeMap.Internal.Impl.link._proof_39 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (id (Eq.refl (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r''))))) (Eq.ndrec (Std.DTreeMap.Internal.Impl.link._proof_41 k v szl k' v' l' r' szr k'' v'' l'' r'') (id (Eq.refl (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))))) snd) snd) _x))) (Eq.refl (PSigma.rec (fun fst snd ↦ PSigma.rec (fun fst snd ↦ PSigma.rec (fun fst snd ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size fst))) fst fst (fun hr ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v fst (Std.DTreeMap.Internal.Impl.link._proof_6 fst snd))) (Std.DTreeMap.Internal.Impl.link._proof_8 k v fst snd) (Std.DTreeMap.Internal.Impl.link._proof_10 k v fst snd)) fun sz k' v' l' r' hr ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) fst snd (fun hr ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 sz k' v' l' r' hr))) (Std.DTreeMap.Internal.Impl.link._proof_14 k v sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.link._proof_16 k v sz k' v' l' r' hr)) fun sz k' v' l' r' hr ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta sz) sz) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 sz k' v' l' r' l' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (PSigma.mk l' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 sz k' v' l' r' hr sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k' v' l' r' hr sz k' v' l' r' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k' v' ℓ r' (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k' v' l' r' hr sz k' v' l' r' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k' v' l' r' hr sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 sz k' v' l' r' hr sz k' v' l' r' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 sz k' v' l' r' hr sz k' v' l' r' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 sz k' v' l' r' hr sz k' v' l' r' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta sz) sz) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' sz k' v' l' r' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k' v' l' r' hr sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 sz k' v' l' r' hr sz k' v' l' r' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k' v' l' r' hr sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k' v' l' r' hr sz k' v' l' r' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 sz k' v' l' r' hr sz k' v' l' r' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 sz k' v' l' r' hr sz k' v' l' r' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 sz k' v' l' r' hr sz k' v' l' r' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd sz (OfNat.ofNat 1)) sz) k v (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v sz k' v' l' r' hr sz k' v' l' r' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v sz k' v' l' r' sz k' v' l' r')) snd) snd) _x))))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.link.eq_def.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ (k : α), ∀ (v : β k), ∀ (l : Std.DTreeMap.Internal.Impl β), ∀ (r : Std.DTreeMap.Internal.Impl β), ∀ (hl : Std.DTreeMap.Internal.Impl.Balanced l), ∀ (hr : Std.DTreeMap.Internal.Impl.Balanced r), Eq (Std.DTreeMap.Internal.Impl.link k v l r hl hr) (Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) l hl (fun hl ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size r)) := Std.DTreeMap.Internal.Impl.insertMin k v r (Std.DTreeMap.Internal.Impl.link._proof_6 r hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v r hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v r hr)) fun szl k' v' l' r' hl ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) r hr (fun hr ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) fun szr k'' v'' l'' r'' hr ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') l'' (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link k v r' (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._proof_39 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._proof_41 k v szl k' v' l' r' szr k'' v'' l'' r'')) := fun {α β} k v l r hl hr ↦ id (Std.DTreeMap.Internal.Impl.link._unary.eq_def k v (PSigma.mk l (PSigma.mk r (PSigma.mk hl hr))))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.toListModel_insertMin.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ [inst : Ord.{u} α], ∀ {k : α}, ∀ {v : β k}, ∀ {t : Std.DTreeMap.Internal.Impl β}, ∀ {h : Std.DTreeMap.Internal.Impl.Balanced t}, Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v t h))) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel t)) := fun {α β} [inst : Ord.{u} #1] {k v t h} ↦ Std.DTreeMap.Internal.Impl.brecOn t (fun {t} f {h} ↦ _private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.toListModel_insertMin.match_1_1 (fun t {h} ↦ ∀ (x : Std.DTreeMap.Internal.Impl.below t), Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v t h))) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel t))) t h (fun h x ↦ Eq.refl (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v (Std.DTreeMap.Internal.Impl.leaf) h)))) (fun size k v l r h x ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl _a)) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)))) (Std.DTreeMap.Internal.Impl.insertMin.eq_2 k v size k v l r h))) (of_eq_true (Eq.trans (congrFun' (congrArg (Eq) (Eq.trans (Std.DTreeMap.Internal.Impl.toListModel_balanceL) (congrFun' (congrArg (HAppend.hAppend) (x.fst.fst (Std.DTreeMap.Internal.Impl.minView._proof_9 size k v l r h))) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (List.cons (Sigma.mk k v) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (eq_self (List.cons (Sigma.mk k v) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))))))) f) h
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) → Std.DTreeMap.Internal.Impl β
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.toListModel_insertMax.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ [inst : Ord.{u} α], ∀ {k : α}, ∀ {v : β k}, ∀ {t : Std.DTreeMap.Internal.Impl β}, ∀ {h : Std.DTreeMap.Internal.Impl.Balanced t}, Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMax k v t h))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel t) (List.cons (Sigma.mk k v) (List.nil))) := fun {α β} [inst : Ord.{u} #1] {k v t h} ↦ Std.DTreeMap.Internal.Impl.brecOn t (fun {t} f {h} ↦ _private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.toListModel_insertMax.match_1_1 (fun t {h} ↦ ∀ (x : Std.DTreeMap.Internal.Impl.below t), Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMax k v t h))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel t) (List.cons (Sigma.mk k v) (List.nil)))) t h (fun h x ↦ Eq.refl (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.leaf) h)))) (fun size k v l r h x ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl _a)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (List.cons (Sigma.mk k v) (List.nil)))) (Std.DTreeMap.Internal.Impl.insertMax.eq_2 k v size k v l r h))) (of_eq_true (Eq.trans (congr (congrArg (Eq) (Eq.trans (Std.DTreeMap.Internal.Impl.toListModel_balanceR) (congrArg (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l)) (congrArg (List.cons (Sigma.mk k v)) (x.snd.fst (Std.DTreeMap.Internal.Impl.minView._proof_11 size k v l r h)))))) (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)) (List.cons (Sigma.mk k v) (List.nil)))) (eq_self (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel r) (List.cons (Sigma.mk k v) (List.nil))))))))) f) h
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) → Std.DTreeMap.Internal.Impl β
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl β) → (r : Std.DTreeMap.Internal.Impl β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl β) x hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)

Test "mlir"

Expected: 👍 accept · Size: 28.8 MB · Lines: 576.3 k · lean4export: 3.1.0 · Lean: 4.27.0-nightly-2025-12-01 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 10.0 s · instructions: 58.7 G · max rss memory: 1.2 GB

stderr:

inductive Com : (d : Dialect) → [DialectSignature d] → Ctxt (Dialect.Ty d) → EffectKind → List.{0} (Dialect.Ty d) → Type
| Com.rets : {d : Dialect} → [inst : DialectSignature d] → {Γ : Ctxt (Dialect.Ty d)} → {tys : List.{0} (Dialect.Ty d)} → {eff : EffectKind} → HVector (Ctxt.Var Γ) tys → Com d Γ eff tys
             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
             invalid return type
theorem Lean.Grind.CommRing.Mon.revlexWF._unary.eq_def : ∀ (_x : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon), Eq (Lean.Grind.CommRing.Mon.revlexWF._unary _x) (PSigma.casesOn _x fun m₁ m₂ ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ x ↦ Ordering) m₁ m₂ (fun _ ↦ Ordering.eq) (fun p m ↦ Ordering.gt) (fun p m ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂))) Ordering.lt) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂)) Ordering.gt))) := fun _x ↦ id (Eq.trans (WellFounded.fix_eq Lean.Grind.CommRing.Mon.revlexWF._unary._proof_1 (fun _x a ↦ PSigma.casesOn _x (fun m₁ m₂ a ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) m₁ m₂ (fun _ x ↦ Ordering.eq) (fun p m x ↦ Ordering.gt) (fun p m x ↦ Ordering.lt) (fun pw₁ m₁ pw₂ m₂ x ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_2 pw₁ m₁ pw₂ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂)) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_3 pw₁ m₁ pw₂ m₂)) Ordering.lt) (Ordering.then (x (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_4 pw₁ m₁ pw₂ m₂)) Ordering.gt))) a) a) _x) (Eq.mpr (id (congrArg (fun x ↦ Eq x (PSigma.rec (fun m₁ m₂ ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ x ↦ Ordering) m₁ m₂ (fun _ ↦ Ordering.eq) (fun p m ↦ Ordering.gt) (fun p m ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂))) Ordering.lt) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂)) Ordering.gt))) _x)) (Eq.trans (_private.Init.Grind.Ring.CommSolver.0.PSigma.casesOn._arg_pusher (PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) (fun _x ↦ Ordering) Lean.Grind.CommRing.Mon.revlexWF._unary (fun _x y ↦ (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y _x) _x fun m₁ m₂ a ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) m₁ m₂ (fun _ x ↦ Ordering.eq) (fun p m x ↦ Ordering.gt) (fun p m x ↦ Ordering.lt) (fun pw₁ m₁ pw₂ m₂ x ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_2 pw₁ m₁ pw₂ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂)) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_3 pw₁ m₁ pw₂ m₂)) Ordering.lt) (Ordering.then (x (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_4 pw₁ m₁ pw₂ m₂)) Ordering.gt))) a) (congrArg (fun x ↦ PSigma.rec x _x) (funext fun fst ↦ funext fun snd ↦ _private.Init.Grind.Ring.CommSolver.0.Lean.Grind.CommRing.Mon.revlexWF.match_1._arg_pusher.{1, 1, 1} (fun m₁ x ↦ Ordering) (PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) (fun _x ↦ Ordering) Lean.Grind.CommRing.Mon.revlexWF._unary (fun m₁ m₂ y ↦ (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂)) fst snd (fun _ x ↦ Ordering.eq) (fun p m x ↦ Ordering.gt) (fun p m x ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ x ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_2 pw₁ m₁ pw₂ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂)) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_3 pw₁ m₁ pw₂ m₂)) Ordering.lt) (Ordering.then (x (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_4 pw₁ m₁ pw₂ m₂)) Ordering.gt))))))) (Eq.refl (PSigma.rec (fun m₁ m₂ ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ x ↦ Ordering) m₁ m₂ (fun _ ↦ Ordering.eq) (fun p m ↦ Ordering.gt) (fun p m ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂))) Ordering.lt) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂)) Ordering.gt))) _x))))
has type
  (p : Lean.Grind.CommRing.Power) → (m : Lean.Grind.CommRing.Mon) → (fun x ↦ (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) (Lean.Grind.CommRing.Mon.mult p m) x) m → ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk (Lean.Grind.CommRing.Mon.mult p m) (Lean.Grind.CommRing.Mon.mult p m)) → Ordering) → Ordering
but is expected to have type
  (p : Lean.Grind.CommRing.Power) → (m : Lean.Grind.CommRing.Mon) → (fun x ↦ (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) (Lean.Grind.CommRing.Mon.mult p m) x) m → (fun x ↦ (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) (Lean.Grind.CommRing.Mon.mult p m) x) (Lean.Grind.CommRing.Mon.mult p m)
theorem Ctxt.Valuation.comap_with : ∀ {Ty : Type}, ∀ [inst : TyDenote Ty], ∀ {ty : List.{0} Ty}, ∀ [inst : DecidableEq.{1} Ty], ∀ {Γ : Ctxt Ty}, ∀ {Δ : Ctxt Ty}, ∀ {V : Ctxt.Valuation Γ}, ∀ {map : Ctxt.Hom Δ Γ}, ∀ {vs : HVector (Ctxt.Var Δ) ty}, ∀ {ws : HVector (Ctxt.Var Γ) ty}, Eq (Ctxt.Valuation.comap V (Ctxt.Hom.with map vs ws)) (Ctxt.Valuation.reassignVars (Ctxt.Valuation.comap V map) vs (HVector.map V ws)) := fun {Ty} [inst : TyDenote #0] {ty} [inst : DecidableEq.{1} #2] {Γ Δ V map vs ws} ↦ funext fun t' ↦ funext fun v' ↦ id (_private.LeanMLIR.ErasedContext.0.Ctxt.Hom.with.match_1.splitter t' (fun x ↦ Eq (HVector.«idxOf?» v' vs) x → Eq (V t' (Ctxt.Hom.with.match_1 t' (fun x ↦ Ctxt.Var Γ t') (HVector.«idxOf?» v' vs) (fun _ ↦ map t' v') fun i h ↦ Ctxt.Var.cast h (HVector.get ws i))) (Ctxt.Hom.with.match_1 t' (fun x ↦ TyDenote.toType t') (HVector.«idxOf?» v' vs) (fun _ ↦ V t' (map t' v')) fun i h ↦ Eq.rec (HVector.get (HVector.map V ws) i) h)) (HVector.«idxOf?» v' vs) (fun x h ↦ Eq.ndrec (fun heq ↦ id (of_eq_true (eq_self (V t' (map t' v'))))) (Eq.symm h) (Eq.refl (HVector.«idxOf?» v' vs))) (fun i h h ↦ Eq.ndrec (fun heq ↦ id (Eq.rec (fun v' x heq ↦ of_eq_true (Eq.trans (congrArg (Eq (V (GetElem.getElem ty (Fin.val i) (Fin.isLt i)) (HVector.get ws i))) (HVector.get_map ws V)) (eq_self (V (GetElem.getElem ty (Fin.val i) (Fin.isLt i)) (HVector.get ws i))))) h v' (HVector.«idxOf?» v' vs) heq)) (Eq.symm h) (Eq.refl (HVector.«idxOf?» v' vs))) (Eq.refl (HVector.«idxOf?» v' vs)))
has type
  ∀ (v' : Ctxt.Var Δ (List.get ty i)), ∀ (x : Option.{0} (Subtype fun i ↦ Eq (List.get ty i) (List.get ty i))), Eq (HVector.«idxOf?» v' vs) (Option.some (Subtype.mk i (Eq.refl (List.get ty i)))) → Eq (V (GetElem.getElem ty (Fin.val i) (Fin.isLt i)) (HVector.get ws i)) (HVector.get (HVector.map V ws) i)
but is expected to have type
  (fun t' h ↦ ∀ (v' : Ctxt.Var Δ t'), ∀ (x : Option.{0} (Subtype fun i ↦ Eq (List.get ty i) t')), Eq (HVector.«idxOf?» v' vs) (Option.some (Subtype.mk i h)) → Eq (V t' (Ctxt.Var.cast h (HVector.get ws i))) (Eq.rec (HVector.get (HVector.map V ws) i) h)) (List.get ty i) (Eq.refl (List.get ty i))
theorem cast_eq_iff_heq.{u_1} : ∀ {a : Sort u_1}, ∀ {a : Sort u_1}, ∀ {e : Eq a a}, ∀ {a : a}, ∀ {a' : a}, Iff (Eq (cast e a) a') (HEq a a') := fun {a a e a a'} ↦ Iff.intro (heq_of_cast_eq e) fun h ↦ HEq.casesOn h (fun h ↦ Eq.ndrec (fun {e a'} h h ↦ Eq.ndrec (fun h h ↦ Eq.refl (cast e a)) (Eq.symm (eq_of_heq h)) h) (Eq.symm h) e a' h) (Eq.refl a) (HEq.refl a') (HEq.refl h)
has type
  ∀ (h : HEq a a), HEq h (HEq.refl a) → Eq (cast e a) (cast e a)
but is expected to have type
  (fun {a'} ↦ ∀ (h : HEq a a'), HEq h (HEq.refl a) → Eq (cast e a) a') a
theorem Expr.changeVars_castCodomain : ∀ {d : Dialect}, ∀ [inst : DialectSignature d], ∀ {Γ : Ctxt (Dialect.Ty d)}, ∀ {eff : EffectKind}, ∀ {t : List.{0} (Dialect.Ty d)}, ∀ {Δ : Ctxt (Dialect.Ty d)}, ∀ {Δ' : Ctxt (Dialect.Ty d)}, ∀ (e : Expr d Γ eff t), ∀ (f : Ctxt.Hom Γ Δ), ∀ (h : Eq Δ Δ'), Eq (Expr.changeVars (Ctxt.Hom.castCodomain h f) e) (cast (of_eq_true (Eq.trans (congrArg (fun x ↦ Eq (Expr d x eff t) (Expr d Δ' eff t)) h) (eq_self (Expr d Δ' eff t)))) (Expr.changeVars f e)) := fun {d} [inst : DialectSignature #0] {Γ eff t Δ Δ'} e f h ↦ Eq.rec (Eq.refl (Expr.changeVars (Ctxt.Hom.castCodomain (Eq.refl Δ) f) e)) h
has type
  Eq (Expr.changeVars (Ctxt.Hom.castCodomain (Eq.refl Δ) f) e) (Expr.changeVars (Ctxt.Hom.castCodomain (Eq.refl Δ) f) e)
but is expected to have type
  (fun {Δ'} h ↦ Eq (Expr.changeVars (Ctxt.Hom.castCodomain h f) e) (cast (of_eq_true (Eq.trans (congrArg (fun x ↦ Eq (Expr d x eff t) (Expr d Δ' eff t)) h) (eq_self (Expr d Δ' eff t)))) (Expr.changeVars f e))) Δ (Eq.refl Δ)
checked in 9.878742s

Test "nat-rec-rules"

Expected: ✋ reject · Size: 8.2 KB · Lines: 128 · lean4export: 3.1.0 · Lean: 4.29.0-rc1 · 📄 Declaration

Test result: ✋ rejected · exit code 1 · wall time: 7 ms · instructions: 12.4 M · max rss memory: 7.4 MB

stderr:

recursor Nat.rec.{u_1} : {motive : Nat → Sort u_1} → motive Nat.zero → ((n : Nat) → motive n → motive (Nat.succ n)) → (t : Nat) → motive t
rule for Nat.succ rhs head is not the corresponding minor (expected bvar #1)
checked in 0.000791s

Test "perf/app-lam"

Expected: 👍 accept · Size: 1.2 MB · Lines: 28.6 k · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 180 ms · instructions: 1.1 G · max rss memory: 117.2 MB

stderr:

checked in 0.164303s

Test "perf/grind-ring-5"

Expected: 👍 accept · Size: 9.7 MB · Lines: 199.2 k · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 3.4 s · instructions: 28.5 G · max rss memory: 364.7 MB

stderr:

theorem Lean.Grind.CommRing.Mon.revlexWF._unary.eq_def : ∀ (_x : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon), Eq (Lean.Grind.CommRing.Mon.revlexWF._unary _x) (PSigma.casesOn _x fun m₁ m₂ ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ x ↦ Ordering) m₁ m₂ (fun _ ↦ Ordering.eq) (fun p m ↦ Ordering.gt) (fun p m ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂))) Ordering.lt) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂)) Ordering.gt))) := fun _x ↦ id (Eq.trans (WellFounded.fix_eq Lean.Grind.CommRing.Mon.revlexWF._unary._proof_1 (fun _x a ↦ PSigma.casesOn _x (fun m₁ m₂ a ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) m₁ m₂ (fun _ x ↦ Ordering.eq) (fun p m x ↦ Ordering.gt) (fun p m x ↦ Ordering.lt) (fun pw₁ m₁ pw₂ m₂ x ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_2 pw₁ m₁ pw₂ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂)) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_3 pw₁ m₁ pw₂ m₂)) Ordering.lt) (Ordering.then (x (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_4 pw₁ m₁ pw₂ m₂)) Ordering.gt))) a) a) _x) (Eq.mpr (id (congrFun' (congrArg (Eq) (Eq.trans (_private.Init.Grind.Ring.CommSolver.0.PSigma.casesOn._arg_pusher (PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) (fun _x ↦ Ordering) Lean.Grind.CommRing.Mon.revlexWF._unary (fun _x y ↦ (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y _x) _x fun m₁ m₂ a ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) m₁ m₂ (fun _ x ↦ Ordering.eq) (fun p m x ↦ Ordering.gt) (fun p m x ↦ Ordering.lt) (fun pw₁ m₁ pw₂ m₂ x ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_2 pw₁ m₁ pw₂ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂)) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_3 pw₁ m₁ pw₂ m₂)) Ordering.lt) (Ordering.then (x (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_4 pw₁ m₁ pw₂ m₂)) Ordering.gt))) a) (congrFun' (congrArg (PSigma.rec) (funext fun fst ↦ funext fun snd ↦ _private.Init.Grind.Ring.CommSolver.0.Lean.Grind.CommRing.Mon.revlexWF.match_1._arg_pusher.{1, 1, 1} (fun m₁ x ↦ Ordering) (PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) (fun _x ↦ Ordering) Lean.Grind.CommRing.Mon.revlexWF._unary (fun m₁ m₂ y ↦ (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂)) fst snd (fun _ x ↦ Ordering.eq) (fun p m x ↦ Ordering.gt) (fun p m x ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ x ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_2 pw₁ m₁ pw₂ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (x (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂)) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_3 pw₁ m₁ pw₂ m₂)) Ordering.lt) (Ordering.then (x (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂) (Lean.Grind.CommRing.Mon.revlexWF._unary._proof_4 pw₁ m₁ pw₂ m₂)) Ordering.gt)))) _x))) (PSigma.rec (fun m₁ m₂ ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ x ↦ Ordering) m₁ m₂ (fun _ ↦ Ordering.eq) (fun p m ↦ Ordering.gt) (fun p m ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂))) Ordering.lt) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂)) Ordering.gt))) _x))) (Eq.refl (PSigma.rec (fun m₁ m₂ ↦ Lean.Grind.CommRing.Mon.revlexWF.match_1.{1} (fun m₁ x ↦ Ordering) m₁ m₂ (fun _ ↦ Ordering.eq) (fun p m ↦ Ordering.gt) (fun p m ↦ Ordering.lt) fun pw₁ m₁ pw₂ m₂ ↦ cond (BEq.beq (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ m₂)) (Lean.Grind.CommRing.powerRevlex (Lean.Grind.CommRing.Power.k pw₁) (Lean.Grind.CommRing.Power.k pw₂))) (cond (Nat.blt (Lean.Grind.CommRing.Power.x pw₁) (Lean.Grind.CommRing.Power.x pw₂)) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk m₁ (Lean.Grind.CommRing.Mon.mult pw₂ m₂))) Ordering.lt) (Ordering.then (Lean.Grind.CommRing.Mon.revlexWF._unary (PSigma.mk (Lean.Grind.CommRing.Mon.mult pw₁ m₁) m₂)) Ordering.gt))) _x))))
has type
  (p : Lean.Grind.CommRing.Power) → (m : Lean.Grind.CommRing.Mon) → (fun x ↦ (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) (Lean.Grind.CommRing.Mon.mult p m) x) m → ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk (Lean.Grind.CommRing.Mon.mult p m) (Lean.Grind.CommRing.Mon.mult p m)) → Ordering) → Ordering
but is expected to have type
  (p : Lean.Grind.CommRing.Power) → (m : Lean.Grind.CommRing.Mon) → (fun x ↦ (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) (Lean.Grind.CommRing.Mon.mult p m) x) m → (fun x ↦ (fun m₁ m₂ ↦ ((y : PSigma fun m₁ ↦ Lean.Grind.CommRing.Mon) → (invImage (fun x ↦ PSigma.casesOn x fun m₁ m₂ ↦ Prod.mk m₁ m₂) (Prod.instWellFoundedRelation (sizeOfWFRel) (sizeOfWFRel))).rel y (PSigma.mk m₁ m₂) → Ordering) → Ordering) (Lean.Grind.CommRing.Mon.mult p m) x) (Lean.Grind.CommRing.Mon.mult p m)
checked in 3.342442s

Test "perf/shift-cascade"

Expected: 👍 accept · Size: 256.3 KB · Lines: 5.1 k · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 15 ms · instructions: 48.5 M · max rss memory: 18.5 MB

stderr:

checked in 0.008456s

Test "proj-of-prop"

Expected: ✋ reject · Size: 3.9 KB · Lines: 56 · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

badFalse : False := (Wrapper.mk True.intro).p

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.2 MB

stderr:

theorem badFalse : False := (Wrapper.mk True.intro).p
                                        ^^^^^^^^^^
                                        has type
                                          True
                                        but is expected to have type
                                          False
checked in 0.000572s

Test "std"

Expected: 👍 accept · Size: 526.1 MB · Lines: 10.0 M · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 2.3 m · instructions: 927.2 G · max rss memory: 14.1 GB

stderr:

theorem Std.DTreeMap.Internal.Impl.balanced_glue.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ {l : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {r : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {hl : Std.DTreeMap.Internal.Impl.Balanced l}, ∀ {hr : Std.DTreeMap.Internal.Impl.Balanced r}, ∀ {hlr : Std.DTreeMap.Internal.Impl.BalancedAtRoot (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)}, Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.glue l r hl hr hlr) := fun {α β l r hl hr hlr} ↦ Eq.mpr (id (congrArg (Std.DTreeMap.Internal.Impl.Balanced) (congrArg (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) l hl hlr fun hl hlr ↦ r) (funext fun sz ↦ funext fun k ↦ funext fun v ↦ funext fun l' ↦ funext fun r' ↦ funext fun hl ↦ funext fun hlr ↦ congrArg (Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr fun hr hlr ↦ l) (funext fun sz' ↦ funext fun k' ↦ funext fun v' ↦ funext fun l'' ↦ funext fun r'' ↦ funext fun hr ↦ funext fun hlr ↦ ite_congr (Eq.refl (LT.lt sz sz')) (fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)))) fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)))))))) (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.minView.match_3.splitter r (fun l hl hlr ↦ Eq l l → HEq hl hl → HEq hlr hlr → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) l hl hlr (fun hl hlr ↦ r) fun sz k v l' r' hl hlr ↦ Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr (fun hr hlr ↦ l) fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt sz sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))))) l hl hlr (fun hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id hr) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (fun size k' v' l' r' hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.glue.match_1.splitter size k' v' l' r' (fun r hr hlr ↦ Eq r r → HEq hr hr → HEq hlr hlr → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.glue.match_1 size k' v' l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr (fun hr hlr ↦ Std.DTreeMap.Internal.Impl.inner size k' v' l' r') fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt size sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner size k' v' l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))))) r hr hlr (fun hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (Eq.mpr (id (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1)) (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ And.intro left (And.intro left (And.intro left right))) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (fun sz' k' v' l'' r'' hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (Decidable.casesOn (Nat.decLt size sz') (fun h ↦ Eq.mpr (id (congrArg (Std.DTreeMap.Internal.Impl.Balanced) (if_neg h))) (of_eq_true (Std.DTreeMap.Internal.Impl.balanced_balanceRErase._simp_1 (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))))) fun h ↦ Eq.mpr (id (congrArg (Std.DTreeMap.Internal.Impl.Balanced) (if_pos h))) (of_eq_true (Std.DTreeMap.Internal.Impl.balanced_balanceLErase._simp_1 hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (Eq.refl r) (HEq.refl hr) (HEq.refl hlr))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (Eq.refl l) (HEq.refl hl) (HEq.refl hlr))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) r → (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) (Std.DTreeMap.Internal.Impl.inner size k v l r) r' hlb hlr
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.size_glue.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ {l : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {r : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {hl : Std.DTreeMap.Internal.Impl.Balanced l}, ∀ {hr : Std.DTreeMap.Internal.Impl.Balanced r}, ∀ {hlr : Std.DTreeMap.Internal.Impl.BalancedAtRoot (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)}, Eq (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.glue l r hl hr hlr)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)) := fun {α β l r hl hr hlr} ↦ Eq.mpr (id (congrFun' (congrArg (Eq) (congrArg (Std.DTreeMap.Internal.Impl.size) (congrArg (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) l hl hlr fun hl hlr ↦ r) (funext fun sz ↦ funext fun k ↦ funext fun v ↦ funext fun l' ↦ funext fun r' ↦ funext fun hl ↦ funext fun hlr ↦ congrArg (Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr fun hr hlr ↦ l) (funext fun sz' ↦ funext fun k' ↦ funext fun v' ↦ funext fun l'' ↦ funext fun r'' ↦ funext fun hr ↦ funext fun hlr ↦ ite_congr (Eq.refl (LT.lt sz sz')) (fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)))) fun a ↦ Eq.refl (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)))))))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)))) (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.minView.match_3.splitter r (fun l hl hlr ↦ Eq l l → HEq hl hl → HEq hlr hlr → Eq (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.minView.match_3 r (fun l hl hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) l hl hlr (fun hl hlr ↦ r) fun sz k v l' r' hl hlr ↦ Std.DTreeMap.Internal.Impl.glue.match_1 sz k v l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr (fun hr hlr ↦ l) fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt sz sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner sz k v l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 sz k v l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k v l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 sz k v l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k v l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k v l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 sz k v l' r' hl sz' k' v' l'' r'' hr)).tree))))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r))) l hl hlr (fun hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (id (Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.minView._proof_5 r a))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (fun size k' v' l' r' hl hlr h ↦ Eq.ndrec (fun {hl hlr} h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.glue.match_1.splitter size k' v' l' r' (fun r hr hlr ↦ Eq r r → HEq hr hr → HEq hlr hlr → Eq (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.glue.match_1 size k' v' l' r' (fun r hr hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) r hr hlr (fun hr hlr ↦ Std.DTreeMap.Internal.Impl.inner size k' v' l' r') fun sz' k' v' l'' r'' hr hlr ↦ ite (LT.lt size sz') (Std.DTreeMap.Internal.Impl.balanceLErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.inner size k' v' l' r') (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (Std.DTreeMap.Internal.Impl.balanceRErase (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr))) (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k' v' l' r')) (Std.DTreeMap.Internal.Impl.size r))) r hr hlr (fun hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (id (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr hlr right h ↦ Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.size_glue._proof_1_9 l' r' a) h hlr hlr right) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r'))) (HEq.refl right)) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (fun sz' k' v' l'' r'' hr hlr h ↦ Eq.ndrec (fun {hr} hlr hlr h ↦ Eq.ndrec (fun h ↦ Eq.ndrec (id (Decidable.casesOn (Nat.decLt size sz') (fun h ↦ Eq.mpr (id (congrFun' (congrArg (Eq) (congrArg (Std.DTreeMap.Internal.Impl.size) (if_neg h))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k' v' l' r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r''))))) (Eq.mpr (id (congrFun' (congrArg (Eq) (Eq.trans (Std.DTreeMap.Internal.Impl.size_balanceRErase (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) hr (Std.DTreeMap.Internal.Impl.glue._proof_20 size k' v' l' r' hl sz' k' v' l'' r'' hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (congrFun' (congrArg (HAdd.hAdd) (congrFun' (congrArg (HAdd.hAdd) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.maxView k' v' l' r' (Std.DTreeMap.Internal.Impl.glue._proof_14 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (OfNat.ofNat 1))) sz'))) (HAdd.hAdd size sz'))) (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr hlr h right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr right hlr h h ↦ Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.size_glue._proof_1_11 l' r' l'' r'' a) h hlr right hlr h) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r'))) (HEq.refl right)) h hlr hlr h right) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l'') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r''))) (HEq.refl right)) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr))))) fun h ↦ Eq.mpr (id (congrFun' (congrArg (Eq) (congrArg (Std.DTreeMap.Internal.Impl.size) (if_pos h))) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k' v' l' r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz' k' v' l'' r''))))) (Eq.mpr (id (congrFun' (congrArg (Eq) (Eq.trans (Std.DTreeMap.Internal.Impl.size_balanceLErase hl (Std.DTreeMap.Internal.Impl.glue._proof_10 size k' v' l' r' hl sz' k' v' l'' r'' hr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.balanced_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)) (Std.DTreeMap.Internal.Impl.glue._proof_12 size k' v' l' r' sz' k' v' l'' r'' hr hlr (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree))) (congrArg (HAdd.hAdd (HAdd.hAdd size (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Tree.size_impl (Std.DTreeMap.Internal.Impl.minView k' v' l'' r'' (Std.DTreeMap.Internal.Impl.glue._proof_4 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_6 size k' v' l' r' hl sz' k' v' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_8 size k' v' l' r' hl sz' k' v' l'' r'' hr)).tree)))) (HAdd.hAdd size sz'))) (And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl) (fun left right h ↦ And.casesOn right (fun left right h ↦ And.casesOn right (fun left right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr hlr h right h ↦ Eq.casesOn right (fun h ↦ Eq.ndrec (fun hlr right hlr h h ↦ Decidable.byContradiction fun a ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.size_glue._proof_1_10 l' r' l'' r'' a) h hlr right hlr h) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r'))) (HEq.refl right)) h hlr hlr h right) (Eq.refl (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l'') (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r''))) (HEq.refl right)) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hl))) (Eq.refl right)) (Eq.refl right)) (Eq.refl (Eq.mp (Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1) hr)))))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hr hlr hlr) (Eq.refl r) (HEq.refl hr) (HEq.refl hlr))) (Eq.symm (eq_of_heq h))) (Eq.symm (eq_of_heq h))) (Eq.symm h) hl hlr) (Eq.refl l) (HEq.refl hl) (HEq.refl hlr))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) r → (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) (Std.DTreeMap.Internal.Impl.inner size k v l r) r' hlb hlr
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner sz k v x r')) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v x r')) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r' hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.toListModel_minView.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ {k : α}, ∀ {v : β k}, ∀ {l : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {r : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {hl : Std.DTreeMap.Internal.Impl.Balanced l}, ∀ {hr : Std.DTreeMap.Internal.Impl.Balanced r}, ∀ {hlr : Std.DTreeMap.Internal.Impl.BalancedAtRoot (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)}, Eq (List.cons (Sigma.mk (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr)) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr))) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.View.tree (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr))))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))) := fun {α β k v l r hl hr hlr} ↦ Std.DTreeMap.Internal.Impl.minView.induct (fun {k v l r hl hr hlr} ↦ Eq (List.cons (Sigma.mk (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr)) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr))) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.View.tree (Std.DTreeMap.Internal.Impl.minView k v l r hl hr hlr))))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (fun k v r hr hl hlr ↦ of_eq_true (eq_self (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (fun k v r hr size k' v' l' r' hl hlr dk dv dt hdt hdt' x ih1 ↦ of_eq_true (Eq.trans (congr (congrArg (Eq) (congrArg (List.cons (Sigma.mk (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l' r' (Std.DTreeMap.Internal.Impl.minView._proof_9 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_11 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_13 size k' v' l' r' hl))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l' r' (Std.DTreeMap.Internal.Impl.minView._proof_9 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_11 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_13 size k' v' l' r' hl))))) (Std.DTreeMap.Internal.Impl.toListModel_balanceRErase))) (congrFun' (congrArg (HAppend.hAppend) (Eq.symm ih1)) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (eq_self (List.cons (Sigma.mk (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.minView k' v' l' r' (Std.DTreeMap.Internal.Impl.minView._proof_9 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_11 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_13 size k' v' l' r' hl))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.minView k' v' l' r' (Std.DTreeMap.Internal.Impl.minView._proof_9 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_11 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_13 size k' v' l' r' hl)))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.minView k' v' l' r' (Std.DTreeMap.Internal.Impl.minView._proof_9 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_11 size k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.minView._proof_13 size k' v' l' r' hl)).tree)) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))))) k v l r hl hr hlr
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) → Std.DTreeMap.Internal.Impl.{u, v} α β
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.toListModel_glue.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ {l : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {r : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {hl : Std.DTreeMap.Internal.Impl.Balanced l}, ∀ {hr : Std.DTreeMap.Internal.Impl.Balanced r}, ∀ {hlr : Std.DTreeMap.Internal.Impl.BalancedAtRoot (Std.DTreeMap.Internal.Impl.size l) (Std.DTreeMap.Internal.Impl.size r)}, Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.glue l r hl hr hlr)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (Std.DTreeMap.Internal.Impl.toListModel r)) := fun {α β l r hl hr hlr} ↦ Std.DTreeMap.Internal.Impl.casesOn l (fun size k v l r h ↦ Eq.ndrec (fun {hl hlr} ↦ Std.DTreeMap.Internal.Impl.casesOn r (fun size k v l r h ↦ Eq.ndrec (fun {hr hlr} ↦ id (Decidable.casesOn (Nat.decLt size size) (fun h ↦ Eq.mpr (id (congrFun' (congrArg (Eq) (congrArg (Std.DTreeMap.Internal.Impl.toListModel) (if_neg h))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r))))) (Eq.mpr (id (congrArg (fun _a ↦ Eq _a (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)))) (Std.DTreeMap.Internal.Impl.toListModel_balanceRErase))) (Eq.mpr (id (congrArg (fun _a ↦ Eq (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l r (Std.DTreeMap.Internal.Impl.glue._proof_14 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k v l r hl size k v l r hr)).tree)) _a) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)))) (Eq.symm (List.singleton_append)))) (Eq.mpr (id (congrArg (fun _a ↦ Eq _a (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)))) (Eq.symm (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.maxView k v l r (Std.DTreeMap.Internal.Impl.glue._proof_14 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k v l r hl size k v l r hr)).tree)) (List.cons (Sigma.mk (Std.DTreeMap.Internal.Impl.View.k (Std.DTreeMap.Internal.Impl.maxView k v l r (Std.DTreeMap.Internal.Impl.glue._proof_14 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k v l r hl size k v l r hr))) (Std.DTreeMap.Internal.Impl.View.v (Std.DTreeMap.Internal.Impl.maxView k v l r (Std.DTreeMap.Internal.Impl.glue._proof_14 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_16 size k v l r hl size k v l r hr) (Std.DTreeMap.Internal.Impl.glue._proof_18 size k v l r hl size k v l r hr)))) (List.nil)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)))))) (of_eq_true (Eq.trans (congr (congrArg (Eq) (Eq.trans (congrFun' (congrArg (HAppend.hAppend) (Std.DTreeMap.Internal.Impl.toListModel_maxView)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))))) (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (eq_self (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel r) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))))))))))) fun h ↦ Eq.mpr (id (congrFun' (congrArg (Eq) (congrArg (Std.DTreeMap.Internal.Impl.toListModel) (if_pos h))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r))))) (of_eq_true (Eq.trans (congr (congrArg (Eq) (Eq.trans (Std.DTreeMap.Internal.Impl.toListModel_balanceLErase) (Eq.trans (congrArg (HAppend.hAppend (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (Std.DTreeMap.Internal.Impl.toListModel_minView)) (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))))) (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (eq_self (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel r) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))))))))) (Eq.symm h) hr hlr) (fun h ↦ Eq.ndrec (fun {hr hlr} ↦ of_eq_true (Eq.trans (congrArg (Eq (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))) (List.append_nil (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (eq_self (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))))) (Eq.symm h) hr hlr) (Eq.refl r)) (Eq.symm h) hl hlr) (fun h ↦ Eq.ndrec (fun {hl hlr} ↦ Std.DTreeMap.Internal.Impl.casesOn r (fun size k v l r h ↦ Eq.ndrec (fun {hr hlr} ↦ of_eq_true (eq_self (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (Eq.symm h) hr hlr) (fun h ↦ Eq.ndrec (fun {hr hlr} ↦ of_eq_true (Eq.trans (congrArg (Eq (List.nil)) (List.append_nil (List.nil))) (eq_self (List.nil)))) (Eq.symm h) hr hlr) (Eq.refl r)) (Eq.symm h) hl hlr) (Eq.refl l)
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v x r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v x r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r hlb hlr) r → (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) (Std.DTreeMap.Internal.Impl.inner size k v l r) r hlb hlr
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v x r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v x r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v x r)) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun ll lr hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x r hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.link._unary.eq_def.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ (k : α), ∀ (v : β k), ∀ (_x : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r), Eq (Std.DTreeMap.Internal.Impl.link._unary k v _x) (PSigma.casesOn _x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) l hl (fun hl ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size r)) := Std.DTreeMap.Internal.Impl.insertMin k v r (Std.DTreeMap.Internal.Impl.link._proof_6 r hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v r hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v r hr)) fun szl k' v' l' r' hl ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) r hr (fun hr ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) fun szr k'' v'' l'' r'' hr ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._proof_39 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._proof_41 k v szl k' v' l' r' szr k'' v'' l'' r'')) := fun {α β} k v _x ↦ id (Eq.trans (WellFounded.Nat.fix_eq (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) (fun _x a ↦ PSigma.casesOn _x (fun l r a ↦ PSigma.casesOn r (fun r hl a ↦ PSigma.casesOn hl (fun hl hr a ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk l (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) l hl (fun hl x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size r)) := Std.DTreeMap.Internal.Impl.insertMin k v r (Std.DTreeMap.Internal.Impl.link._proof_6 r hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v r hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v r hr)) (fun szl k' v' l' r' hl x ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) r hr (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) (fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v szl k' v' l' r' szr k'' v'' l'' r'')) x) a) a) a) a) _x) (Eq.mpr (id (congrFun' (congrArg (Eq) (Eq.trans (_private.Std.Data.DTreeMap.Internal.Operations.0.PSigma.casesOn._arg_pusher (PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) (fun _x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size _x.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size _x.snd.fst))) (Std.DTreeMap.Internal.Impl.link._unary k v) (fun _x y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y _x) _x fun l r a ↦ PSigma.casesOn r (fun r hl a ↦ PSigma.casesOn hl (fun hl hr a ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk l (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) l hl (fun hl x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size r)) := Std.DTreeMap.Internal.Impl.insertMin k v r (Std.DTreeMap.Internal.Impl.link._proof_6 r hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v r hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v r hr)) (fun szl k' v' l' r' hl x ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) r hr (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) (fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v szl k' v' l' r' szr k'' v'' l'' r'')) x) a) a) a) (congrFun (congrArg (PSigma.rec) (funext fun fst ↦ funext fun snd ↦ Eq.trans (_private.Std.Data.DTreeMap.Internal.Operations.0.PSigma.casesOn._arg_pusher (PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) (fun _x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size _x.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size _x.snd.fst))) (Std.DTreeMap.Internal.Impl.link._unary k v) (fun r y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk fst r)) snd fun r hl a ↦ PSigma.casesOn hl (fun hl hr a ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk l (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) fst hl (fun hl x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size r)) := Std.DTreeMap.Internal.Impl.insertMin k v r (Std.DTreeMap.Internal.Impl.link._proof_6 r hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v r hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v r hr)) (fun szl k' v' l' r' hl x ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) r hr (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) (fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v szl k' v' l' r' szr k'' v'' l'' r'')) x) a) a) (congrFun (congrArg (PSigma.rec) (funext fun fst ↦ funext fun snd ↦ Eq.trans (_private.Std.Data.DTreeMap.Internal.Operations.0.PSigma.casesOn._arg_pusher (PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) (fun _x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size _x.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size _x.snd.fst))) (Std.DTreeMap.Internal.Impl.link._unary k v) (fun hl y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk fst (PSigma.mk fst hl))) snd fun hl hr a ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk l (PSigma.mk fst (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size fst))) fst hl (fun hl x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size fst)) := Std.DTreeMap.Internal.Impl.insertMin k v fst (Std.DTreeMap.Internal.Impl.link._proof_6 fst hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v fst hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v fst hr)) (fun szl k' v' l' r' hl x ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) fst hr (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) (fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v szl k' v' l' r' szr k'' v'' l'' r'')) x) a) (congrFun (congrArg (PSigma.rec) (funext fun fst ↦ funext fun snd ↦ Eq.trans (_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.insertMin.match_3._arg_pusher (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size fst))) (PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) (fun _x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size _x.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size _x.snd.fst))) (Std.DTreeMap.Internal.Impl.link._unary k v) (fun l hl y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk l (PSigma.mk fst (PSigma.mk hl snd)))) fst fst (fun hl x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size fst)) := Std.DTreeMap.Internal.Impl.insertMin k v fst (Std.DTreeMap.Internal.Impl.link._proof_6 fst snd)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v fst snd) (Std.DTreeMap.Internal.Impl.link._proof_10 k v fst snd)) fun szl k' v' l' r' hl x ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ ((y : PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) → InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk r (PSigma.mk hl hr))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size y.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size y.snd.fst))) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) fst snd (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) (fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v szl k' v' l' r' szr k'' v'' l'' r'')) x) (congrArg (Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size fst))) fst fst fun hr ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v fst (Std.DTreeMap.Internal.Impl.link._proof_6 fst snd))) (Std.DTreeMap.Internal.Impl.link._proof_8 k v fst snd) (Std.DTreeMap.Internal.Impl.link._proof_10 k v fst snd)) (funext fun sz ↦ funext fun k' ↦ funext fun v' ↦ funext fun l' ↦ funext fun r' ↦ funext fun hr ↦ _private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.insertMin.match_3._arg_pusher (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) (PSigma fun l ↦ PSigma fun r ↦ PSigma fun hl ↦ Std.DTreeMap.Internal.Impl.Balanced r) (fun _x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size _x.fst) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size _x.snd.fst))) (Std.DTreeMap.Internal.Impl.link._unary k v) (fun r hr y ↦ InvImage (fun x1 x2 ↦ LT.lt x1 x2) (fun x ↦ PSigma.casesOn x fun l r ↦ PSigma.casesOn r fun r hl ↦ PSigma.casesOn hl fun hl hr ↦ HAdd.hAdd (SizeOf.sizeOf l) (SizeOf.sizeOf r)) y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (PSigma.mk r (PSigma.mk hr hr)))) fst snd (fun hr x ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 sz k' v' l' r' hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.link._proof_16 k v sz k' v' l' r' hr)) fun szr k'' v'' l'' r'' hr x ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta sz) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 sz k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 sz k' v' l' r' hr szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k' v' l' r' hr szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_1 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k' v' l' r' hr szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k' v' l' r' hr szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) sz) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (x (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k' v' l' r' hr szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 sz k' v' l' r' hr szr k'' v'' l'' r'' hr)))) (Std.DTreeMap.Internal.Impl.link._unary._proof_2 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₂)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k' v' l' r' hr szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k' v' l' r' hr szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd sz (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v sz k' v' l' r' hr szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v sz k' v' l' r' szr k'' v'' l'' r''))))) snd))) snd))) _x))) (PSigma.rec (fun fst snd ↦ PSigma.rec (fun fst snd ↦ PSigma.rec (fun fst snd ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size fst))) fst fst (fun hr ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v fst (Std.DTreeMap.Internal.Impl.link._proof_6 fst snd))) (Std.DTreeMap.Internal.Impl.link._proof_8 k v fst snd) (Std.DTreeMap.Internal.Impl.link._proof_10 k v fst snd)) fun szl k' v' l' r' hl ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) fst snd (fun hr ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl))) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) fun szr k'' v'' l'' r'' hr ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (PSigma.mk l'' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Eq.ndrec (Std.DTreeMap.Internal.Impl.link._proof_39 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (id (Eq.refl (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r''))))) (Eq.ndrec (Std.DTreeMap.Internal.Impl.link._proof_41 k v szl k' v' l' r' szr k'' v'' l'' r'') (id (Eq.refl (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))))) snd) snd) _x))) (Eq.refl (PSigma.rec (fun fst snd ↦ PSigma.rec (fun fst snd ↦ PSigma.rec (fun fst snd ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size fst))) fst fst (fun hr ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v fst (Std.DTreeMap.Internal.Impl.link._proof_6 fst snd))) (Std.DTreeMap.Internal.Impl.link._proof_8 k v fst snd) (Std.DTreeMap.Internal.Impl.link._proof_10 k v fst snd)) fun sz k' v' l' r' hr ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) fst snd (fun hr ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 sz k' v' l' r' hr))) (Std.DTreeMap.Internal.Impl.link._proof_14 k v sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.link._proof_16 k v sz k' v' l' r' hr)) fun sz k' v' l' r' hr ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta sz) sz) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 sz k' v' l' r' l' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (PSigma.mk l' (PSigma.mk (Std.DTreeMap.Internal.Impl.link._proof_18 sz k' v' l' r' hr sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 sz k' v' l' r' hr sz k' v' l' r' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k' v' ℓ r' (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k' v' l' r' hr sz k' v' l' r' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 sz k' v' l' r' hr sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 sz k' v' l' r' hr sz k' v' l' r' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 sz k' v' l' r' hr sz k' v' l' r' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 sz k' v' l' r' hr sz k' v' l' r' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta sz) sz) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' sz k' v' l' r' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')))) (Std.DTreeMap.Internal.Impl.link._unary k v (PSigma.mk r' (PSigma.mk (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (PSigma.mk (Std.DTreeMap.Internal.Impl.glue._proof_16 sz k' v' l' r' hr sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 sz k' v' l' r' hr sz k' v' l' r' hr))))) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 sz k' v' l' r' hr sz k' v' l' r' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 sz k' v' l' r' hr sz k' v' l' r' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 sz k' v' l' r' hr sz k' v' l' r' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 sz k' v' l' r' hr sz k' v' l' r' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 sz k' v' l' r' hr sz k' v' l' r' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd sz (OfNat.ofNat 1)) sz) k v (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r') (Std.DTreeMap.Internal.Impl.inner sz k' v' l' r')) (Std.DTreeMap.Internal.Impl.link._unary._proof_3 k v sz k' v' l' r' hr sz k' v' l' r' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._unary._proof_4 k v sz k' v' l' r' sz k' v' l' r')) snd) snd) _x))))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.link.eq_def.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ (k : α), ∀ (v : β k), ∀ (l : Std.DTreeMap.Internal.Impl.{u, v} α β), ∀ (r : Std.DTreeMap.Internal.Impl.{u, v} α β), ∀ (hl : Std.DTreeMap.Internal.Impl.Balanced l), ∀ (hr : Std.DTreeMap.Internal.Impl.Balanced r), Eq (Std.DTreeMap.Internal.Impl.link k v l r hl hr) (Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun l hl ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size l) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) l hl (fun hl ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (OfNat.ofNat 1) (Std.DTreeMap.Internal.Impl.size r)) := Std.DTreeMap.Internal.Impl.insertMin k v r (Std.DTreeMap.Internal.Impl.link._proof_6 r hr)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_8 k v r hr) (Std.DTreeMap.Internal.Impl.link._proof_10 k v r hr)) fun szl k' v' l' r' hl ↦ Std.DTreeMap.Internal.Impl.insertMin.match_3 (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) r hr (fun hr ↦ let d : Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) := Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.link._proof_12 szl k' v' l' r' hl)
Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.Tree.impl d) (Std.DTreeMap.Internal.Impl.link._proof_14 k v szl k' v' l' r' hl) (Std.DTreeMap.Internal.Impl.link._proof_16 k v szl k' v' l' r' hl)) fun szr k'' v'' l'' r'' hr ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szl) szr) (fun h₁ ↦ Std.DTreeMap.Internal.Impl.link.match_1 szl k' v' l' r' l'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') l'' (Std.DTreeMap.Internal.Impl.link._proof_18 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_4 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceLErase k'' v'' ℓ r'' (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.glue._proof_6 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_21 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_23 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_26 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ ℓ hℓ₁ hℓ₂)) fun h₁ ↦ dite (LT.lt (HMul.hMul Std.DTreeMap.Internal.delta szr) szl) (fun h₂ ↦ Std.DTreeMap.Internal.Impl.link.match_3 r' szr k'' v'' l'' r'' (fun x ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r')) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')))) (Std.DTreeMap.Internal.Impl.link k v r' (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'') (Std.DTreeMap.Internal.Impl.glue._proof_16 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.link._proof_28 szl k' v' l' r' hl szr k'' v'' l'' r'' hr)) fun ℓ hℓ₁ hℓ₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.balanceRErase k' v' l' ℓ (Std.DTreeMap.Internal.Impl.glue._proof_14 szl k' v' l' r' hl szr k'' v'' l'' r'' hr) (Std.DTreeMap.Internal.Impl.glue._proof_10 szl k' v' l' r' hl szr k'' v'' l'' r'' hr ℓ hℓ₁) (Std.DTreeMap.Internal.Impl.link._proof_31 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₂)) (Std.DTreeMap.Internal.Impl.link._proof_33 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂) (Std.DTreeMap.Internal.Impl.link._proof_36 szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂ ℓ hℓ₁ hℓ₂)) fun h₂ ↦ Std.DTreeMap.Internal.Impl.Tree.mk (Std.DTreeMap.Internal.Impl.inner (HAdd.hAdd (HAdd.hAdd szl (OfNat.ofNat 1)) szr) k v (Std.DTreeMap.Internal.Impl.inner szl k' v' l' r') (Std.DTreeMap.Internal.Impl.inner szr k'' v'' l'' r'')) (Std.DTreeMap.Internal.Impl.link._proof_39 k v szl k' v' l' r' hl szr k'' v'' l'' r'' hr h₁ h₂) (Std.DTreeMap.Internal.Impl.link._proof_41 k v szl k' v' l' r' szr k'' v'' l'' r'')) := fun {α β} k v l r hl hr ↦ id (Std.DTreeMap.Internal.Impl.link._unary.eq_def k v (PSigma.mk l (PSigma.mk r (PSigma.mk hl hr))))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (fun r hr ↦ Std.DTreeMap.Internal.Impl.Tree.{u, v} α β (HAdd.hAdd (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (OfNat.ofNat 1)) (Std.DTreeMap.Internal.Impl.size r))) x hr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.toListModel_insertMin.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ [inst : Ord.{u} α], ∀ {k : α}, ∀ {v : β k}, ∀ {t : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {h : Std.DTreeMap.Internal.Impl.Balanced t}, Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v t h))) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel t)) := fun {α β} [inst : Ord.{u} #1] {k v t h} ↦ Std.DTreeMap.Internal.Impl.brecOn t (fun {t} f {h} ↦ _private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.toListModel_insertMin.match_1_1 (fun t {h} ↦ ∀ (x : Std.DTreeMap.Internal.Impl.below t), Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v t h))) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel t))) t h (fun h x ↦ Eq.refl (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMin k v (Std.DTreeMap.Internal.Impl.leaf) h)))) (fun size k v l r h x ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl _a)) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)))) (Std.DTreeMap.Internal.Impl.insertMin.eq_2 k v size k v l r h))) (of_eq_true (Eq.trans (congrFun' (congrArg (Eq) (Eq.trans (Std.DTreeMap.Internal.Impl.toListModel_balanceL) (congrFun' (congrArg (HAppend.hAppend) (x.fst.fst (Std.DTreeMap.Internal.Impl.minView._proof_9 size k v l r h))) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (List.cons (Sigma.mk k v) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r))))) (eq_self (List.cons (Sigma.mk k v) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)))))))) f) h
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) → Std.DTreeMap.Internal.Impl.{u, v} α β
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.toListModel_insertMax.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ [inst : Ord.{u} α], ∀ {k : α}, ∀ {v : β k}, ∀ {t : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {h : Std.DTreeMap.Internal.Impl.Balanced t}, Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMax k v t h))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel t) (List.cons (Sigma.mk k v) (List.nil))) := fun {α β} [inst : Ord.{u} #1] {k v t h} ↦ Std.DTreeMap.Internal.Impl.brecOn t (fun {t} f {h} ↦ _private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.toListModel_insertMax.match_1_1 (fun t {h} ↦ ∀ (x : Std.DTreeMap.Internal.Impl.below t), Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMax k v t h))) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel t) (List.cons (Sigma.mk k v) (List.nil)))) t h (fun h x ↦ Eq.refl (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl (Std.DTreeMap.Internal.Impl.insertMax k v (Std.DTreeMap.Internal.Impl.leaf) h)))) (fun size k v l r h x ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.Tree.impl _a)) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel (Std.DTreeMap.Internal.Impl.inner size k v l r)) (List.cons (Sigma.mk k v) (List.nil)))) (Std.DTreeMap.Internal.Impl.insertMax.eq_2 k v size k v l r h))) (of_eq_true (Eq.trans (congr (congrArg (Eq) (Eq.trans (Std.DTreeMap.Internal.Impl.toListModel_balanceR) (congrArg (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l)) (congrArg (List.cons (Sigma.mk k v)) (x.snd.fst (Std.DTreeMap.Internal.Impl.minView._proof_11 size k v l r h)))))) (List.append_assoc (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (Std.DTreeMap.Internal.Impl.toListModel r)) (List.cons (Sigma.mk k v) (List.nil)))) (eq_self (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel l) (List.cons (Sigma.mk k v) (HAppend.hAppend (Std.DTreeMap.Internal.Impl.toListModel r) (List.cons (Sigma.mk k v) (List.nil))))))))) f) h
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) → Std.DTreeMap.Internal.Impl.{u, v} α β
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) l → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) r → (fun x ↦ (hlb : Std.DTreeMap.Internal.Impl.Balanced x) → (hlr : Std.DTreeMap.Internal.Impl.BalanceLPrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → (fun l hlb hlr ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hlb hlr) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.alter_eq_alterₘ.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ [inst : Ord.{u} α], ∀ [inst : Std.TransOrd α], ∀ [inst : Std.LawfulEqOrd α], ∀ {t : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {a : α}, ∀ {f : Option.{v} (β a) → Option.{v} (β a)}, ∀ (htb : Std.DTreeMap.Internal.Impl.Balanced t), Std.DTreeMap.Internal.Impl.Ordered t → Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f t htb)) (Std.DTreeMap.Internal.Impl.alterₘ a f t htb) := fun {α β} [inst : Ord.{u} #1] [inst : Std.TransOrd #2] [inst : Std.LawfulEqOrd #3] {t a f} htb hto ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f t htb)) _a) (Std.DTreeMap.Internal.Impl.alterₘ.eq_1 a f t htb))) (Std.DTreeMap.Internal.Impl.rec (fun sz k v l r ihl ihr htb hto ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) (Std.DTreeMap.Internal.Impl.inner sz k v l r) htb))) (Std.DTreeMap.Internal.Impl.alter.eq_2 a f sz k v l r htb))) (Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_13 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_15 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_18 sz k v l r htb d hd hd'₁ hd'₂)) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_20 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_22 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_25 sz k v l r htb d hd hd'₁ hd'₂)) fun h ↦ Std.DTreeMap.Internal.Impl.«getThenInsertIfNew?».match_1 a (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k h) v))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_13 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.erase._proof_34 sz k v l r htb) (Std.DTreeMap.Internal.Impl.erase._proof_36 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_28 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.alter._proof_30 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_33 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_35 a sz k v l r htb v))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a)) (Std.DTreeMap.Internal.Impl.updateCell.eq_2 a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) sz k v l r htb))) (_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.alter.match_3.splitter.{0} (fun x ↦ Eq (Ord.compare a k) x → Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_13 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_15 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_18 sz k v l r htb d hd hd'₁ hd'₂)) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_20 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_22 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_25 sz k v l r htb d hd hd'₁ hd'₂)) fun h ↦ Std.DTreeMap.Internal.Impl.«getThenInsertIfNew?».match_1 a (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans (Eq.refl (Ord.compare a k)) h)) v))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_13 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.erase._proof_34 sz k v l r htb) (Std.DTreeMap.Internal.Impl.erase._proof_36 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_28 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.alter._proof_30 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_33 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_35 a sz k v l r htb v))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_3 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)) fun newL h₁ h₂ h₃ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v newL r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb newL h₁) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb newL h₂ h₃)) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb newL h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb newL h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb newL h₁ h₂ h₃)) (fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')) fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_3 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)) fun newR h₁ h₂ h₃ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l newR (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb newR h₁) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb newR h₂ h₃)) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb newR h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb newR h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb newR h₁ h₂ h₃)))) (Ord.compare a k) (fun h h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (of_eq_true (Eq.trans (congrFun' (congrArg (Eq) (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.Balanced.left htb))) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto)) r r (Eq.refl r) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))))) (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (eq_self (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.Balanced.left htb))) r (Eq.ndrec (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto))) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Eq.ndrec (Eq.ndrec (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (Eq.refl r)) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto))))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun h h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (of_eq_true (Eq.trans (congrFun' (congrArg (Eq) (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) l l (Eq.refl l) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto)) (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))))) (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))))) (eq_self (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Eq.ndrec (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto))) (Eq.ndrec (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a f r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto))))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun h h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.«getThenInsertIfNew?».match_1 a (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans heq (Eq.refl Ordering.eq))) v))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_13 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.erase._proof_34 sz k v l r htb) (Std.DTreeMap.Internal.Impl.erase._proof_36 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_28 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.alter._proof_30 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_33 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_35 a sz k v l r htb v)))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (fun x ↦ Std.DTreeMap.Internal.Cell.alter f x) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (Eq.symm (id (Option.casesOn (f (Option.some (Eq.rec v (Std.DTreeMap.Internal.Cell.alter._proof_1 (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq (Eq.refl Ordering.eq)) k v (Eq.refl (Option.some (Sigma.mk k v))))))) (fun h ↦ Eq.ndrec (fun h₁ ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.ofOption.match_1 a (fun «v?» ↦ Std.DTreeMap.Internal.Cell α β (Ord.compare a)) (Option.none) (fun _ ↦ Std.DTreeMap.Internal.Cell.empty) fun v ↦ Std.DTreeMap.Internal.Cell.of a v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')))) (Eq.symm h) (Eq.refl (f (Option.some (Eq.rec v (Std.DTreeMap.Internal.Cell.alter._proof_1 (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq (Eq.refl Ordering.eq)) k v (Eq.refl (Option.some (Sigma.mk k v))))))))) (fun val h ↦ Eq.ndrec (fun h₁ ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.ofOption.match_1 a (fun «v?» ↦ Std.DTreeMap.Internal.Cell α β (Ord.compare a)) (Option.some val) (fun _ ↦ Std.DTreeMap.Internal.Cell.empty) fun v ↦ Std.DTreeMap.Internal.Cell.of a v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')))) (Eq.symm h) (Eq.refl (f (Option.some (Eq.rec v (Std.DTreeMap.Internal.Cell.alter._proof_1 (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq (Eq.refl Ordering.eq)) k v (Eq.refl (Option.some (Sigma.mk k v))))))))) (Eq.refl (f (Option.some (Eq.rec v (Std.DTreeMap.Internal.Cell.alter._proof_1 (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq (Eq.refl Ordering.eq)) k v (Eq.refl (Option.some (Sigma.mk k v))))))))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (Eq.refl (Ord.compare a k))))) (fun htb hto ↦ id (Option.casesOn (f (Option.none)) (fun h ↦ Eq.ndrec (of_eq_true (eq_self (Std.DTreeMap.Internal.Impl.leaf))) (Eq.symm h)) (fun val h ↦ Eq.ndrec (of_eq_true (eq_self (Std.DTreeMap.Internal.Impl.inner (OfNat.ofNat 1) a val (Std.DTreeMap.Internal.Impl.leaf) (Std.DTreeMap.Internal.Impl.leaf)))) (Eq.symm h)) (Eq.refl (f (Option.none))))) t htb hto)
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hr h) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → Std.DTreeMap.Internal.Impl.{u, v} α β
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hr h) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hr h) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.Const.alter_eq_alterₘ.{u, v} : ∀ {α : Type u}, ∀ {β : Type v}, ∀ [inst : Ord.{u} α], ∀ [inst : Std.TransOrd α], ∀ {t : Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β}, ∀ {a : α}, ∀ {f : Option.{v} β → Option.{v} β}, ∀ (htb : Std.DTreeMap.Internal.Impl.Balanced t), Std.DTreeMap.Internal.Impl.Ordered t → Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f t htb)) (Std.DTreeMap.Internal.Impl.Const.alterₘ a f t htb) := fun {α β} [inst : Ord.{u} #1] [inst : Std.TransOrd #2] {t a f} htb hto ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f t htb)) _a) (Std.DTreeMap.Internal.Impl.Const.alterₘ.eq_1 a f t htb))) (Std.DTreeMap.Internal.Impl.rec (fun sz k v l r ihl ihr htb hto ↦ Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) (Std.DTreeMap.Internal.Impl.inner sz k v l r) htb))) (Std.DTreeMap.Internal.Impl.Const.alter.eq_2 a f sz k v l r htb))) (Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_24 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_27 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_30 sz k v l r htb d hd hd'₁ hd'₂)) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_32 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_35 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_38 sz k v l r htb d hd hd'₁ hd'₂)) fun _ ↦ Std.DTreeMap.Internal.Impl.Const.«getThenInsertIfNew?».match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_40 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_42 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_45 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_48 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_50 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_53 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_56 a sz k v l r htb v))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a)) (Std.DTreeMap.Internal.Impl.updateCell.eq_2 a (Std.DTreeMap.Internal.Cell.Const.alter f) sz k v l r htb))) (_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.insert.match_3.splitter.{0} (fun x ↦ Eq (Ord.compare a k) x → Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_24 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_27 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_30 sz k v l r htb d hd hd'₁ hd'₂)) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_32 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_35 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_38 sz k v l r htb d hd hd'₁ hd'₂)) fun _ ↦ Std.DTreeMap.Internal.Impl.Const.«getThenInsertIfNew?».match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_40 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_42 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_45 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_48 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_50 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_53 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_56 a sz k v l r htb v))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_3 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)) fun newL h₁ h₂ h₃ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v newL r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb newL h₁) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb newL h₂ h₃)) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb newL h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb newL h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb newL h₁ h₂ h₃)) (fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.Const.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')) fun h ↦ Std.DTreeMap.Internal.Impl.updateCell.match_3 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)) fun newR h₁ h₂ h₃ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l newR (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb newR h₁) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb newR h₂ h₃)) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb newR h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb newR h₁ h₂ h₃) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb newR h₁ h₂ h₃)))) (Ord.compare a k) (fun a h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.Const.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (of_eq_true (Eq.trans (congrFun' (congrArg (Eq) (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.Balanced.left htb))) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto)) r r (Eq.refl r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))))) (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (eq_self (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.Balanced.left htb))) r (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Eq.ndrec (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (Eq.refl r)) (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb) (Std.DTreeMap.Internal.Impl.Ordered.left hto))))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun a h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.Const.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (of_eq_true (Eq.trans (congrFun' (congrArg (Eq) (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) l l (Eq.refl l) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))))) (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))))) (eq_self (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto))) (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a f r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb) (Std.DTreeMap.Internal.Impl.Ordered.right hto))))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun a h ↦ Eq.ndrec (fun heq ↦ id (Eq.mpr (id (congrArg (Eq (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.«getThenInsertIfNew?».match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (f (Option.some v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_40 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_42 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_45 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_48 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_50 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_53 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_56 a sz k v l r htb v)))) (congrArg (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl) (Std.DTreeMap.Internal.Impl.applyPartition.go.match_1.congr heq (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) r (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_32 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_34 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_37 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_40 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) l (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb)))))) (fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.Const.alter f (Std.DTreeMap.Internal.Cell.ofEq k v fun [Std.OrientedOrd α] ↦ Eq.trans heq h))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y'))) fun h ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_27 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_61 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))) (Std.DTreeMap.Internal.Impl.updateCell._proof_63 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_66 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.updateCell._proof_69 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.updateCell a (Std.DTreeMap.Internal.Cell.Const.alter f) r (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb))))))))) (Eq.symm (id (Option.casesOn (f (Option.some v)) (fun h ↦ Eq.ndrec (fun h₁ ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.ofOption.match_1 a (fun «v?» ↦ Std.DTreeMap.Internal.Cell α (fun x ↦ β) (Ord.compare a)) (Option.none) (fun _ ↦ Std.DTreeMap.Internal.Cell.empty) fun v ↦ Std.DTreeMap.Internal.Cell.of a v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')))) (Eq.symm h) (Eq.refl (f (Option.some v)))) (fun val h ↦ Eq.ndrec (fun h₁ ↦ Eq.refl (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.updateCell.match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Cell.inner (Std.DTreeMap.Internal.Cell.ofOption.match_1 a (fun «v?» ↦ Std.DTreeMap.Internal.Cell α (fun x ↦ β) (Ord.compare a)) (Option.some val) (fun _ ↦ Std.DTreeMap.Internal.Cell.empty) fun v ↦ Std.DTreeMap.Internal.Cell.of a v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.updateCell._proof_25 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_29 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_42 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.updateCell._proof_44 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_47 sz k v l r htb) (Std.DTreeMap.Internal.Impl.updateCell._proof_50 sz k v l r htb)) fun ky' y' ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz ky' y' l r) (Std.DTreeMap.Internal.Impl.updateCell._proof_52 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_55 sz k v l r htb ky' y') (Std.DTreeMap.Internal.Impl.updateCell._proof_58 sz k v l r htb ky' y')))) (Eq.symm h) (Eq.refl (f (Option.some v)))) (Eq.refl (f (Option.some v)))))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (Eq.refl (Ord.compare a k))))) (fun htb hto ↦ id (Option.casesOn (f (Option.none)) (fun h ↦ Eq.ndrec (of_eq_true (eq_self (Std.DTreeMap.Internal.Impl.leaf))) (Eq.symm h)) (fun val h ↦ Eq.ndrec (of_eq_true (eq_self (Std.DTreeMap.Internal.Impl.inner (OfNat.ofNat 1) a val (Std.DTreeMap.Internal.Impl.leaf) (Std.DTreeMap.Internal.Impl.leaf)))) (Eq.symm h)) (Eq.refl (f (Option.none))))) t htb hto)
has type
  (size : Nat) → (k : α) → (v : (fun x ↦ β) k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) x hr h) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β
but is expected to have type
  (size : Nat) → (k : α) → (v : (fun x ↦ β) k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) x hr h) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) x hr h) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.modify_eq_alter.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ [inst : Ord.{u} α], ∀ [inst : Std.LawfulEqOrd α], ∀ {t : Std.DTreeMap.Internal.Impl.{u, v} α β}, ∀ {a : α}, ∀ {f : β a → β a}, ∀ (htb : Std.DTreeMap.Internal.Impl.Balanced t), Eq (Std.DTreeMap.Internal.Impl.modify a f t) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) t htb)) := fun {α β} [inst : Ord.{u} #1] [inst : Std.LawfulEqOrd #2] {t a f} htb ↦ Std.DTreeMap.Internal.Impl.rec (fun sz k v l r ihl ihr htb ↦ let hmb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.modify a f (Std.DTreeMap.Internal.Impl.inner sz k v l r)) := Std.DTreeMap.Internal.Impl.balanced_modify htb
Eq.mpr (id (congrArg (fun _a ↦ Eq _a (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) (Std.DTreeMap.Internal.Impl.inner sz k v l r) htb))) (Std.DTreeMap.Internal.Impl.modify.eq_2 a f sz k v l r))) (Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.modify a f l) r) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.modify a f r)) fun h ↦ Std.DTreeMap.Internal.Impl.inner sz a (f (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k h) v)) l r) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a)) (Std.DTreeMap.Internal.Impl.alter.eq_2 a (fun x ↦ Option.map f x) sz k v l r htb))) (_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.alter.match_3.splitter.{0} (fun x ↦ Eq (Ord.compare a k) x → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.modify a f l) r) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.modify a f r)) fun h ↦ Std.DTreeMap.Internal.Impl.inner sz a (f (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans (Eq.refl (Ord.compare a k)) h)) v)) l r) → Eq (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.modify a f l) r) (fun h ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.modify a f r)) fun h ↦ Std.DTreeMap.Internal.Impl.inner sz a (f (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans (Eq.refl (Ord.compare a k)) h)) v)) l r) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_13 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_15 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_18 sz k v l r htb d hd hd'₁ hd'₂)) (fun h ↦ Std.DTreeMap.Internal.Impl.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.alter._proof_20 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_22 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.alter._proof_25 sz k v l r htb d hd hd'₁ hd'₂)) fun h ↦ Std.DTreeMap.Internal.Impl.«getThenInsertIfNew?».match_1 a (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α β (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Option.map f (Option.some (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans (Eq.refl (Ord.compare a k)) h)) v))) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_13 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.erase._proof_34 sz k v l r htb) (Std.DTreeMap.Internal.Impl.erase._proof_36 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_28 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.alter._proof_30 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_33 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.alter._proof_35 a sz k v l r htb v)))) (Ord.compare a k) (fun h h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ of_eq_true (Eq.trans (congrArg (Eq (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.modify a f l) r)) (Eq.trans (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.modify a f l) (Eq.symm (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb))) r r (Eq.refl r) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb) (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))))) ((fun x_0 ↦ (fun x_0 ↦ Std.DTreeMap.Internal.Impl.balance_eq_inner hmb) x_0) (Eq.ndrec (Eq.ndrec (Std.DTreeMap.Internal.Impl.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb)))) (Eq.refl r)) (Eq.symm (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb))))))) (eq_self (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.modify a f l) r)))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun h h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ of_eq_true (Eq.trans (congrArg (Eq (Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.modify a f r))) (Eq.trans (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) l l (Eq.refl l) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.modify a f r) (Eq.symm (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (Std.DTreeMap.Internal.Impl.minView._proof_9 sz k v l r htb) (Std.DTreeMap.Internal.Impl.minView._proof_15 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))))) ((fun x_0 ↦ (fun x_0 ↦ Std.DTreeMap.Internal.Impl.balance_eq_inner hmb) x_0) (Eq.ndrec (Std.DTreeMap.Internal.Impl.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.minView._proof_11 sz k v l r htb)))) (Eq.symm (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb))))))) (eq_self (Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.modify a f r))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun h h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ Eq.refl (Std.DTreeMap.Internal.Impl.inner sz a (f (cast (Std.DTreeMap.Internal.Impl.alter._proof_3 a k (Eq.trans heq (Eq.refl Ordering.eq))) v)) l r)) (Eq.symm h) (Eq.refl (Ord.compare a k))) (Eq.refl (Ord.compare a k)) (Eq.mp (congrArg (fun l ↦ Std.DTreeMap.Internal.Impl.Balanced l) (Std.DTreeMap.Internal.Impl.modify.eq_2 a f sz k v l r)) hmb)))) (fun htb ↦ Eq.refl (Std.DTreeMap.Internal.Impl.modify a f (Std.DTreeMap.Internal.Impl.leaf))) t htb
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hr h) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → Std.DTreeMap.Internal.Impl.{u, v} α β
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hr h) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α β) x hr h) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.Const.modify_eq_alter.{u, v} : ∀ {α : Type u}, ∀ {β : Type v}, ∀ [inst : Ord.{u} α], [Std.TransOrd α] → ∀ {t : Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β}, ∀ {a : α}, ∀ {f : β → β}, ∀ (htb : Std.DTreeMap.Internal.Impl.Balanced t), Eq (Std.DTreeMap.Internal.Impl.Const.modify a f t) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) t htb)) := fun {α β} [inst : Ord.{u} #1] [inst : Std.TransOrd #2] {t a f} htb ↦ Std.DTreeMap.Internal.Impl.rec (fun sz k v l r ihl ihr htb ↦ let hmb : Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.Const.modify a f (Std.DTreeMap.Internal.Impl.inner sz k v l r)) := Std.DTreeMap.Internal.Impl.Const.balanced_modify htb
Eq.mpr (id (congrArg (fun _a ↦ Eq _a (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) (Std.DTreeMap.Internal.Impl.inner sz k v l r) htb))) (Std.DTreeMap.Internal.Impl.Const.modify.eq_2 a f sz k v l r))) (Eq.mpr (id (congrArg (fun _a ↦ Eq (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.Const.modify a f l) r) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.Const.modify a f r)) fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz a (f v) l r) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl _a)) (Std.DTreeMap.Internal.Impl.Const.alter.eq_2 a (fun x ↦ Option.map f x) sz k v l r htb))) (_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.insert.match_3.splitter.{0} (fun x ↦ Eq (Ord.compare a k) x → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.Const.modify a f l) r) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.Const.modify a f r)) fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz a (f v) l r) → Eq (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.Const.modify a f l) r) (fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.Const.modify a f r)) fun _ ↦ Std.DTreeMap.Internal.Impl.inner sz a (f v) l r) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.insert.match_3.{(max u v) + 1} (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Ord.compare a k) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 l (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v d r (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_24 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_27 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_30 sz k v l r htb d hd hd'₁ hd'₂)) (fun _ ↦ Std.DTreeMap.Internal.Impl.Const.alter.match_1 r (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)) fun d hd hd'₁ hd'₂ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.balance k v l d (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb d hd) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb d hd'₁ hd'₂)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_32 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_35 sz k v l r htb d hd hd'₁ hd'₂) (Std.DTreeMap.Internal.Impl.Const.alter._proof_38 sz k v l r htb d hd hd'₁ hd'₂)) fun _ ↦ Std.DTreeMap.Internal.Impl.Const.«getThenInsertIfNew?».match_1 (fun x ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.{u, v} α (fun x ↦ β) (HSub.hSub (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1)) (HAdd.hAdd (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner sz k v l r)) (OfNat.ofNat 1))) (Option.map f (Option.some v)) (fun _ ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.glue l r (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_40 sz k v l r htb)) (Std.DTreeMap.Internal.Impl.Const.alter._proof_42 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_45 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_48 sz k v l r htb)) fun v ↦ Std.DTreeMap.Internal.Impl.SizedBalancedTree.mk (Std.DTreeMap.Internal.Impl.inner sz a v l r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_50 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_53 a sz k v l r htb v) (Std.DTreeMap.Internal.Impl.Const.alter._proof_56 a sz k v l r htb v)))) (Ord.compare a k) (fun a h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ id (of_eq_true (Eq.trans (congrArg (Eq (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.Const.modify a f l) r)) (Eq.trans (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.Const.modify a f l) (Eq.symm (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb))) r r (Eq.refl r) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))))) ((fun x_0 ↦ (fun x_0 ↦ Std.DTreeMap.Internal.Impl.balance_eq_inner hmb) x_0) (Eq.ndrec (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_1 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) l (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb)))) (Eq.refl r)) (Eq.symm (ihl (Std.DTreeMap.Internal.Impl.Balanced.left htb))))))) (eq_self (Std.DTreeMap.Internal.Impl.inner sz k v (Std.DTreeMap.Internal.Impl.Const.modify a f l) r))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun a h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ id (of_eq_true (Eq.trans (congrArg (Eq (Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.Const.modify a f r))) (Eq.trans (Std.DTreeMap.Internal.Impl.balance.congr_simp k v v (Eq.refl v) l l (Eq.refl l) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.Const.modify a f r) (Eq.symm (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_18 sz k v l r htb) (Std.DTreeMap.Internal.Impl.Const.alter._proof_20 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.balanced_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))))) ((fun x_0 ↦ (fun x_0 ↦ Std.DTreeMap.Internal.Impl.balance_eq_inner hmb) x_0) (Eq.ndrec (Std.DTreeMap.Internal.Impl.Const.alter._proof_2 sz k v l r htb (Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.lb_le_size_impl (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb))) (Std.DTreeMap.Internal.Impl.SizedBalancedTree.size_impl_le_ub (Std.DTreeMap.Internal.Impl.Const.alter a (fun x ↦ Option.map f x) r (Std.DTreeMap.Internal.Impl.Const.alter._proof_22 sz k v l r htb)))) (Eq.symm (ihr (Std.DTreeMap.Internal.Impl.Balanced.right htb))))))) (eq_self (Std.DTreeMap.Internal.Impl.inner sz k v l (Std.DTreeMap.Internal.Impl.Const.modify a f r)))))) (Eq.symm h) (Eq.refl (Ord.compare a k))) (fun a h ↦ Eq.ndrec (fun heq ↦ id fun hmb ↦ Eq.refl (Std.DTreeMap.Internal.Impl.inner sz a (f v) l r)) (Eq.symm h) (Eq.refl (Ord.compare a k))) (Eq.refl (Ord.compare a k)) (Eq.mp (congrArg (fun _a ↦ Std.DTreeMap.Internal.Impl.Balanced _a) (Std.DTreeMap.Internal.Impl.Const.modify.eq_2 a f sz k v l r)) hmb)))) (fun htb ↦ Eq.refl (Std.DTreeMap.Internal.Impl.Const.modify a f (Std.DTreeMap.Internal.Impl.leaf))) t htb
has type
  (size : Nat) → (k : α) → (v : (fun x ↦ β) k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) x hr h) r → Std.DTreeMap.Internal.Impl.Balanced (Std.DTreeMap.Internal.Impl.inner size k v l r) → Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r))) → Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β
but is expected to have type
  (size : Nat) → (k : α) → (v : (fun x ↦ β) k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) x hr h) l → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) x hr h) r → (fun x ↦ (hr : Std.DTreeMap.Internal.Impl.Balanced x) → (h : Or (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)) (Std.DTreeMap.Internal.Impl.size x)) (Std.DTreeMap.Internal.Impl.BalanceLErasePrecond (Std.DTreeMap.Internal.Impl.size x) (Std.DTreeMap.Internal.Impl.size (Std.DTreeMap.Internal.Impl.inner size k v l r)))) → (fun r hr h ↦ Std.DTreeMap.Internal.Impl.{u, v} α fun x ↦ β) x hr h) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.«minKey!».eq_def.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ [inst : Inhabited.{u + 1} α], ∀ (x : Std.DTreeMap.Internal.Impl.{u, v} α β), Eq (Std.DTreeMap.Internal.Impl.«minKey!» x) (Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ α) x (fun _ ↦ panicWithPosWithDecl "Std.Data.DTreeMap.Internal.Queries" "Std.DTreeMap.Internal.Impl.minKey!" (OfNat.ofNat 413) (OfNat.ofNat 13) "Map is empty") (fun size k v r ↦ k) fun size k v l size k v l r h r ↦ Std.DTreeMap.Internal.Impl.«minKey!» l) := fun {α β} [inst : Inhabited.{u + 1} #1] x ↦ id (Eq.trans (WellFounded.fix_eq (Std.DTreeMap.Internal.Impl.«minKey!»._proof_1) (fun a a ↦ Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → α) → α) a (fun _ x ↦ panicWithPosWithDecl "Std.Data.DTreeMap.Internal.Queries" "Std.DTreeMap.Internal.Impl.minKey!" (OfNat.ofNat 413) (OfNat.ofNat 13) "Map is empty") (fun size k v r x ↦ k) (fun size k v l size k v l r h r x ↦ x l (Std.DTreeMap.Internal.Impl.«minKey!»._proof_2 size k v l size k v l r h r)) a) x) (Eq.mpr (id (congrFun' (congrArg (Eq) (_private.Std.Data.DTreeMap.Internal.Queries.0.Std.DTreeMap.Internal.Impl.«minEntry?».match_1._arg_pusher (fun x ↦ α) (Std.DTreeMap.Internal.Impl.{u, v} α β) (fun x ↦ α) (Std.DTreeMap.Internal.Impl.«minKey!») (fun x y ↦ (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x) x (fun _ x ↦ panicWithPosWithDecl "Std.Data.DTreeMap.Internal.Queries" "Std.DTreeMap.Internal.Impl.minKey!" (OfNat.ofNat 413) (OfNat.ofNat 13) "Map is empty") (fun size k v r x ↦ k) fun size k v l size k v l r h r x ↦ x l (Std.DTreeMap.Internal.Impl.«minKey!»._proof_2 size k v l size k v l r h r))) (Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ α) x (fun _ ↦ panicWithPosWithDecl "Std.Data.DTreeMap.Internal.Queries" "Std.DTreeMap.Internal.Impl.minKey!" (OfNat.ofNat 413) (OfNat.ofNat 13) "Map is empty") (fun size k v r ↦ k) fun size k v l size k v l r h r ↦ Std.DTreeMap.Internal.Impl.«minKey!» l))) (Eq.refl (Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ α) x (fun _ ↦ panicWithPosWithDecl "Std.Data.DTreeMap.Internal.Queries" "Std.DTreeMap.Internal.Impl.minKey!" (OfNat.ofNat 413) (OfNat.ofNat 13) "Map is empty") (fun size k v r ↦ k) fun size k v l size k v l r h r ↦ Std.DTreeMap.Internal.Impl.«minKey!» l))))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r)) l → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r)) r → ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y (Std.DTreeMap.Internal.Impl.inner size k v (namedPattern (Std.DTreeMap.Internal.Impl.inner size k v l r) (Std.DTreeMap.Internal.Impl.inner size k v l r) (Eq.refl (Std.DTreeMap.Internal.Impl.inner size k v l r))) r) → α) → α
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r)) l → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r)) r → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.«minKey?».eq_def.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ (x : Std.DTreeMap.Internal.Impl.{u, v} α β), Eq (Std.DTreeMap.Internal.Impl.«minKey?» x) (Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ Option.{u} α) x (fun _ ↦ Option.none) (fun size k v r ↦ Option.some k) fun size k v l size k v l r h r ↦ Std.DTreeMap.Internal.Impl.«minKey?» l) := fun {α β} x ↦ id (Eq.trans (WellFounded.fix_eq (Std.DTreeMap.Internal.Impl.«minKey?»._proof_1) (fun a a ↦ Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{u} α) → Option.{u} α) a (fun _ x ↦ Option.none) (fun size k v r x ↦ Option.some k) (fun size k v l size k v l r h r x ↦ x l (Std.DTreeMap.Internal.Impl.«minKey?»._proof_2 size k v l size k v l r h r)) a) x) (Eq.mpr (id (congrFun' (congrArg (Eq) (_private.Std.Data.DTreeMap.Internal.Queries.0.Std.DTreeMap.Internal.Impl.«minEntry?».match_1._arg_pusher (fun x ↦ Option.{u} α) (Std.DTreeMap.Internal.Impl.{u, v} α β) (fun x ↦ Option.{u} α) (Std.DTreeMap.Internal.Impl.«minKey?») (fun x y ↦ (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x) x (fun _ x ↦ Option.none) (fun size k v r x ↦ Option.some k) fun size k v l size k v l r h r x ↦ x l (Std.DTreeMap.Internal.Impl.«minKey?»._proof_2 size k v l size k v l r h r))) (Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ Option.{u} α) x (fun _ ↦ Option.none) (fun size k v r ↦ Option.some k) fun size k v l size k v l r h r ↦ Std.DTreeMap.Internal.Impl.«minKey?» l))) (Eq.refl (Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ Option.{u} α) x (fun _ ↦ Option.none) (fun size k v r ↦ Option.some k) fun size k v l size k v l r h r ↦ Std.DTreeMap.Internal.Impl.«minKey?» l))))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{u} α) → Option.{u} α) (Std.DTreeMap.Internal.Impl.inner size k v x r)) l → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{u} α) → Option.{u} α) (Std.DTreeMap.Internal.Impl.inner size k v x r)) r → ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y (Std.DTreeMap.Internal.Impl.inner size k v (namedPattern (Std.DTreeMap.Internal.Impl.inner size k v l r) (Std.DTreeMap.Internal.Impl.inner size k v l r) (Eq.refl (Std.DTreeMap.Internal.Impl.inner size k v l r))) r) → Option.{u} α) → Option.{u} α
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{u} α) → Option.{u} α) (Std.DTreeMap.Internal.Impl.inner size k v x r)) l → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{u} α) → Option.{u} α) (Std.DTreeMap.Internal.Impl.inner size k v x r)) r → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{u} α) → Option.{u} α) (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.«minEntry?».eq_def.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ (x : Std.DTreeMap.Internal.Impl.{u, v} α β), Eq (Std.DTreeMap.Internal.Impl.«minEntry?» x) (Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) x (fun _ ↦ Option.none) (fun size k v r ↦ Option.some (Sigma.mk k v)) fun size k v l size k v l r h r ↦ Std.DTreeMap.Internal.Impl.«minEntry?» l) := fun {α β} x ↦ id (Eq.trans (WellFounded.fix_eq (Std.DTreeMap.Internal.Impl.«minEntry?»._proof_1) (fun a a ↦ Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) a (fun _ x ↦ Option.none) (fun size k v r x ↦ Option.some (Sigma.mk k v)) (fun size k v l size k v l r h r x ↦ x l (Std.DTreeMap.Internal.Impl.«minEntry?»._proof_2 size k v l size k v l r h r)) a) x) (Eq.mpr (id (congrFun' (congrArg (Eq) (_private.Std.Data.DTreeMap.Internal.Queries.0.Std.DTreeMap.Internal.Impl.«minEntry?».match_1._arg_pusher (fun x ↦ Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) (Std.DTreeMap.Internal.Impl.{u, v} α β) (fun x ↦ Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) (Std.DTreeMap.Internal.Impl.«minEntry?») (fun x y ↦ (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x) x (fun _ x ↦ Option.none) (fun size k v r x ↦ Option.some (Sigma.mk k v)) fun size k v l size k v l r h r x ↦ x l (Std.DTreeMap.Internal.Impl.«minEntry?»._proof_2 size k v l size k v l r h r))) (Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) x (fun _ ↦ Option.none) (fun size k v r ↦ Option.some (Sigma.mk k v)) fun size k v l size k v l r h r ↦ Std.DTreeMap.Internal.Impl.«minEntry?» l))) (Eq.refl (Std.DTreeMap.Internal.Impl.«minEntry?».match_1 (fun x ↦ Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) x (fun _ ↦ Option.none) (fun size k v r ↦ Option.some (Sigma.mk k v)) fun size k v l size k v l r h r ↦ Std.DTreeMap.Internal.Impl.«minEntry?» l))))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) (Std.DTreeMap.Internal.Impl.inner size k v x r)) l → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) (Std.DTreeMap.Internal.Impl.inner size k v x r)) r → ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y (Std.DTreeMap.Internal.Impl.inner size k v (namedPattern (Std.DTreeMap.Internal.Impl.inner size k v l r) (Std.DTreeMap.Internal.Impl.inner size k v l r) (Eq.refl (Std.DTreeMap.Internal.Impl.inner size k v l r))) r) → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) (Std.DTreeMap.Internal.Impl.inner size k v x r)) l → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) (Std.DTreeMap.Internal.Impl.inner size k v x r)) r → (fun x ↦ (fun x ↦ ((y : Std.DTreeMap.Internal.Impl.{u, v} α β) → (invImage (fun x ↦ x) (sizeOfWFRel)).rel y x → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) → Option.{(max v u)} (Sigma.{u, v} α fun a ↦ β a)) (Std.DTreeMap.Internal.Impl.inner size k v x r)) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.minKey._unary.eq_def.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ (_x : PSigma fun t ↦ Eq (Std.DTreeMap.Internal.Impl.isEmpty t) Bool.false), Eq (Std.DTreeMap.Internal.Impl.minKey._unary _x) (PSigma.casesOn _x fun t h ↦ Std.DTreeMap.Internal.Impl.minEntry.match_1 (fun x x ↦ α) t h (fun size k v r x ↦ k) fun size k v l size k v l r h r h ↦ Std.DTreeMap.Internal.Impl.minKey._unary (PSigma.mk l (Std.DTreeMap.Internal.Impl.minEntry._proof_5 l size k v l r h))) := fun {α β} _x ↦ id (Eq.trans (WellFounded.fix_eq (Std.DTreeMap.Internal.Impl.minKey._unary._proof_1) (fun _x a ↦ PSigma.casesOn _x (fun t h a ↦ Std.DTreeMap.Internal.Impl.minEntry.match_1 (fun x x ↦ ((y : PSigma fun t ↦ Eq (Std.DTreeMap.Internal.Impl.isEmpty t) Bool.false) → (invImage (fun x ↦ PSigma.casesOn x fun t h ↦ t) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) t h (fun size k v r x x ↦ k) (fun size k v l size k v l r h r h x ↦ x (PSigma.mk l (Std.DTreeMap.Internal.Impl.minEntry._proof_5 l size k v l r h)) (Std.DTreeMap.Internal.Impl.minKey._unary._proof_2 size k v l size k v l r h r h)) a) a) _x) (Eq.mpr (id (congrFun' (congrArg (Eq) (Eq.trans (_private.Std.Data.DTreeMap.Internal.Queries.0.PSigma.casesOn._arg_pusher (PSigma fun t ↦ Eq (Std.DTreeMap.Internal.Impl.isEmpty t) Bool.false) (fun _x ↦ α) (Std.DTreeMap.Internal.Impl.minKey._unary) (fun _x y ↦ (invImage (fun x ↦ PSigma.casesOn x fun t h ↦ t) (sizeOfWFRel)).rel y _x) _x fun t h a ↦ Std.DTreeMap.Internal.Impl.minEntry.match_1 (fun x x ↦ ((y : PSigma fun t ↦ Eq (Std.DTreeMap.Internal.Impl.isEmpty t) Bool.false) → (invImage (fun x ↦ PSigma.casesOn x fun t h ↦ t) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) t h (fun size k v r x x ↦ k) (fun size k v l size k v l r h r h x ↦ x (PSigma.mk l (Std.DTreeMap.Internal.Impl.minEntry._proof_5 l size k v l r h)) (Std.DTreeMap.Internal.Impl.minKey._unary._proof_2 size k v l size k v l r h r h)) a) (congrFun' (congrArg (PSigma.rec) (funext fun fst ↦ funext fun snd ↦ _private.Std.Data.DTreeMap.Internal.Queries.0.Std.DTreeMap.Internal.Impl.minEntry.match_1._arg_pusher (fun x x ↦ α) (PSigma fun t ↦ Eq (Std.DTreeMap.Internal.Impl.isEmpty t) Bool.false) (fun _x ↦ α) (Std.DTreeMap.Internal.Impl.minKey._unary) (fun x x y ↦ (invImage (fun x ↦ PSigma.casesOn x fun t h ↦ t) (sizeOfWFRel)).rel y (PSigma.mk x x)) fst snd (fun size k v r x x ↦ k) fun size k v l size k v l r h r h x ↦ x (PSigma.mk l (Std.DTreeMap.Internal.Impl.minEntry._proof_5 l size k v l r h)) (Std.DTreeMap.Internal.Impl.minKey._unary._proof_2 size k v l size k v l r h r h))) _x))) (PSigma.rec (fun t h ↦ Std.DTreeMap.Internal.Impl.minEntry.match_1 (fun x x ↦ α) t h (fun size k v r x ↦ k) fun size k v l size k v l r h r h ↦ Std.DTreeMap.Internal.Impl.minKey._unary (PSigma.mk l (Std.DTreeMap.Internal.Impl.minEntry._proof_5 l size k v l r h))) _x))) (Eq.refl (PSigma.rec (fun t h ↦ Std.DTreeMap.Internal.Impl.minEntry.match_1 (fun x x ↦ α) t h (fun size k v r x ↦ k) fun size k v l size k v l r h r h ↦ Std.DTreeMap.Internal.Impl.minKey._unary (PSigma.mk l (Std.DTreeMap.Internal.Impl.minEntry._proof_5 l size k v l r h))) _x))))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (x : Eq (Std.DTreeMap.Internal.Impl.isEmpty (Std.DTreeMap.Internal.Impl.inner size k v x r)) Bool.false) → (fun x x ↦ ((y : PSigma fun t ↦ Eq (Std.DTreeMap.Internal.Impl.isEmpty t) Bool.false) → (invImage (fun x ↦ PSigma.casesOn x fun t h ↦ t) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r) x) l → (fun x ↦ (x : Eq (Std.DTreeMap.Internal.Impl.isEmpty (Std.DTreeMap.Internal.Impl.inner size k v x r)) Bool.false) → (fun x x ↦ ((y : PSigma fun t ↦ Eq (Std.DTreeMap.Internal.Impl.isEmpty t) Bool.false) → (invImage (fun x ↦ PSigma.casesOn x fun t h ↦ t) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r) x) r → (x : Eq (Std.DTreeMap.Internal.Impl.isEmpty (Std.DTreeMap.Internal.Impl.inner size k v (Std.DTreeMap.Internal.Impl.inner size k v l r) r)) Bool.false) → ((y : PSigma fun t ↦ Eq (Std.DTreeMap.Internal.Impl.isEmpty t) Bool.false) → (invImage (fun x ↦ PSigma.casesOn x fun t h ↦ t) (sizeOfWFRel)).rel y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner size k v (namedPattern (Std.DTreeMap.Internal.Impl.inner size k v l r) (Std.DTreeMap.Internal.Impl.inner size k v l r) (Eq.refl (Std.DTreeMap.Internal.Impl.inner size k v l r))) r) x) → α) → α
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (x : Eq (Std.DTreeMap.Internal.Impl.isEmpty (Std.DTreeMap.Internal.Impl.inner size k v x r)) Bool.false) → (fun x x ↦ ((y : PSigma fun t ↦ Eq (Std.DTreeMap.Internal.Impl.isEmpty t) Bool.false) → (invImage (fun x ↦ PSigma.casesOn x fun t h ↦ t) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r) x) l → (fun x ↦ (x : Eq (Std.DTreeMap.Internal.Impl.isEmpty (Std.DTreeMap.Internal.Impl.inner size k v x r)) Bool.false) → (fun x x ↦ ((y : PSigma fun t ↦ Eq (Std.DTreeMap.Internal.Impl.isEmpty t) Bool.false) → (invImage (fun x ↦ PSigma.casesOn x fun t h ↦ t) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r) x) r → (fun x ↦ (x : Eq (Std.DTreeMap.Internal.Impl.isEmpty (Std.DTreeMap.Internal.Impl.inner size k v x r)) Bool.false) → (fun x x ↦ ((y : PSigma fun t ↦ Eq (Std.DTreeMap.Internal.Impl.isEmpty t) Bool.false) → (invImage (fun x ↦ PSigma.casesOn x fun t h ↦ t) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r) x) (Std.DTreeMap.Internal.Impl.inner size k v l r)
theorem Std.DTreeMap.Internal.Impl.minKeyD._unary.eq_def.{u, v} : ∀ {α : Type u}, ∀ {β : α → Type v}, ∀ (_x : PSigma fun a ↦ α), Eq (Std.DTreeMap.Internal.Impl.minKeyD._unary _x) (PSigma.casesOn _x fun a a ↦ Std.DTreeMap.Internal.Impl.minKeyD.match_1 (fun x x ↦ α) a a (fun h ↦ h) (fun size k v r x ↦ k) fun size k v l size k v l r h r fallback ↦ Std.DTreeMap.Internal.Impl.minKeyD._unary (PSigma.mk l fallback)) := fun {α β} _x ↦ id (Eq.trans (WellFounded.fix_eq (Std.DTreeMap.Internal.Impl.minKeyD._unary._proof_1) (fun _x a ↦ PSigma.casesOn _x (fun a a a ↦ Std.DTreeMap.Internal.Impl.minKeyD.match_1 (fun x x ↦ ((y : PSigma fun x ↦ α) → (invImage (fun x ↦ PSigma.casesOn x fun a a ↦ a) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) a a (fun fallback x ↦ fallback) (fun size k v r x x ↦ k) (fun size k v l size k v l r h r fallback x ↦ x (PSigma.mk l fallback) (Std.DTreeMap.Internal.Impl.minKeyD._unary._proof_2 size k v l size k v l r h r fallback)) a) a) _x) (Eq.mpr (id (congrFun' (congrArg (Eq) (Eq.trans (_private.Std.Data.DTreeMap.Internal.Queries.0.PSigma.casesOn._arg_pusher (PSigma fun a ↦ α) (fun _x ↦ α) (Std.DTreeMap.Internal.Impl.minKeyD._unary) (fun _x y ↦ (invImage (fun x ↦ PSigma.casesOn x fun a x ↦ a) (sizeOfWFRel)).rel y _x) _x fun a a a ↦ Std.DTreeMap.Internal.Impl.minKeyD.match_1 (fun x x ↦ ((y : PSigma fun x1 ↦ α) → (invImage (fun x ↦ PSigma.casesOn x fun a a ↦ a) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) a a (fun fallback x ↦ fallback) (fun size k v r x x ↦ k) (fun size k v l size k v l r h r fallback x ↦ x (PSigma.mk l fallback) (Std.DTreeMap.Internal.Impl.minKeyD._unary._proof_2 size k v l size k v l r h r fallback)) a) (congrFun' (congrArg (PSigma.rec) (funext fun fst ↦ funext fun snd ↦ _private.Std.Data.DTreeMap.Internal.Queries.0.Std.DTreeMap.Internal.Impl.minKeyD.match_1._arg_pusher (fun x x ↦ α) (PSigma fun x1 ↦ α) (fun _x ↦ α) (Std.DTreeMap.Internal.Impl.minKeyD._unary) (fun x x y ↦ (invImage (fun x ↦ PSigma.casesOn x fun a x ↦ a) (sizeOfWFRel)).rel y (PSigma.mk x x)) fst snd (fun fallback x ↦ fallback) (fun size k v r x x ↦ k) fun size k v l size k v l r h r fallback x ↦ x (PSigma.mk l fallback) (Std.DTreeMap.Internal.Impl.minKeyD._unary._proof_2 size k v l size k v l r h r fallback))) _x))) (PSigma.rec (fun a a ↦ Std.DTreeMap.Internal.Impl.minKeyD.match_1 (fun x x ↦ α) a a (fun h ↦ h) (fun size k v r x ↦ k) fun size k v l size k v l r h r fallback ↦ Std.DTreeMap.Internal.Impl.minKeyD._unary (PSigma.mk l fallback)) _x))) (Eq.refl (PSigma.rec (fun a a ↦ Std.DTreeMap.Internal.Impl.minKeyD.match_1 (fun x x ↦ α) a a (fun h ↦ h) (fun size k v r x ↦ k) fun size k v l size k v l r h r fallback ↦ Std.DTreeMap.Internal.Impl.minKeyD._unary (PSigma.mk l fallback)) _x))))
has type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (fun x x ↦ ((y : PSigma fun x1 ↦ α) → (invImage (fun x ↦ PSigma.casesOn x fun a a ↦ a) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r) _x.snd) l → (fun x ↦ (fun x x ↦ ((y : PSigma fun x1 ↦ α) → (invImage (fun x ↦ PSigma.casesOn x fun a a ↦ a) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r) _x.snd) r → ((y : PSigma fun a ↦ α) → (invImage (fun x ↦ PSigma.casesOn x fun a x ↦ a) (sizeOfWFRel)).rel y (PSigma.mk (Std.DTreeMap.Internal.Impl.inner size k v (namedPattern (Std.DTreeMap.Internal.Impl.inner size k v l r) (Std.DTreeMap.Internal.Impl.inner size k v l r) (Eq.refl (Std.DTreeMap.Internal.Impl.inner size k v l r))) r) _x.snd) → α) → α
but is expected to have type
  (size : Nat) → (k : α) → (v : β k) → (l : Std.DTreeMap.Internal.Impl.{u, v} α β) → (r : Std.DTreeMap.Internal.Impl.{u, v} α β) → (fun x ↦ (fun x x ↦ ((y : PSigma fun x1 ↦ α) → (invImage (fun x ↦ PSigma.casesOn x fun a a ↦ a) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r) _x.snd) l → (fun x ↦ (fun x x ↦ ((y : PSigma fun x1 ↦ α) → (invImage (fun x ↦ PSigma.casesOn x fun a a ↦ a) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r) _x.snd) r → (fun x ↦ (fun x x ↦ ((y : PSigma fun x1 ↦ α) → (invImage (fun x ↦ PSigma.casesOn x fun a a ↦ a) (sizeOfWFRel)).rel y (PSigma.mk x x) → α) → α) (Std.DTreeMap.Internal.Impl.inner size k v x r) _x.snd) (Std.DTreeMap.Internal.Impl.inner size k v l r)

Test "tutorial/001_basicDef"

Expected: 👍 accept · Size: 371 B · Lines: 6 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 22 ms · instructions: 20.1 M · max rss memory: 7.0 MB

stderr:

checked in 0.001516s

Test "tutorial/002_badDef"

Expected: ✋ reject · Size: 369 B · Lines: 6 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.1 MB

stderr:

def badDef : Prop :=
  Type
  ^^^^
  has type
    Type 1
  but is expected to have type
    Prop
checked in 0.000380s

Test "tutorial/003_arrowType"

Expected: 👍 accept · Size: 626 B · Lines: 12 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 7.1 MB

stderr:

checked in 0.000314s

Test "tutorial/004_dependentType"

Expected: 👍 accept · Size: 464 B · Lines: 7 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 7.1 MB

stderr:

checked in 0.000350s

Test "tutorial/005_constType"

Expected: 👍 accept · Size: 901 B · Lines: 17 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000269s

Test "tutorial/006_betaReduction"

Expected: 👍 accept · Size: 1.3 KB · Lines: 27 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000413s

Test "tutorial/007_betaReduction2"

Expected: 👍 accept · Size: 1.4 KB · Lines: 28 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000419s

Test "tutorial/008_forallSortWhnf"

Expected: 👍 accept · Size: 1.2 KB · Lines: 25 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000419s

Test "tutorial/009_forallSortBad"

Expected: ✋ reject · Size: 1.2 KB · Lines: 26 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

def forallSortBad : Prop :=
  ∀ (x : id Prop), ∀ (x : x), x → x
                          ^
                          has type
                            x
                          but is expected to be a Sort (Type or Prop)
checked in 0.000453s

Test "tutorial/010_nonTypeType"

Expected: ✋ reject · Size: 1.1 KB · Lines: 21 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

def nonTypeType : constType :=
                  ^^^^^^^^^
                  has type
                    Type → Type → Type
                  but is expected to be a Sort (Type or Prop)
checked in 0.000387s

Test "tutorial/011_nonPropThm"

Expected: ✋ reject · Size: 428 B · Lines: 7 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.1 MB

stderr:

theorem nonPropThm : Prop := ∀ (x : Prop), x
                     ^^^^
                     has sort
                       Type
                     but the type of a theorem must be a proposition (Prop)
checked in 0.000375s

Test "tutorial/012_levelComp1"

Expected: 👍 accept · Size: 395 B · Lines: 7 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 7.0 MB

stderr:

checked in 0.000295s

Test "tutorial/013_levelComp2"

Expected: 👍 accept · Size: 413 B · Lines: 8 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 7.0 MB

stderr:

checked in 0.000309s

Test "tutorial/014_levelComp3"

Expected: 👍 accept · Size: 431 B · Lines: 9 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 7.1 MB

stderr:

checked in 0.000320s

Test "tutorial/015_levelParams"

Expected: 👍 accept · Size: 1.4 KB · Lines: 29 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000398s

Test "tutorial/016_tut06_bad01"

Expected: ✋ reject · Size: 431 B · Lines: 8 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 7 ms · instructions: 11.5 M · max rss memory: 6.9 MB

stderr:

Invalid declaration tut06_bad01.{u, u}: duplicate level parameter u

checked in 0.000373s

Test "tutorial/017_levelComp4"

Expected: 👍 accept · Size: 428 B · Lines: 8 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 7.0 MB

stderr:

checked in 0.000323s

Test "tutorial/018_levelComp5"

Expected: 👍 accept · Size: 428 B · Lines: 8 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 7.0 MB

stderr:

checked in 0.000320s

Test "tutorial/019_imax1"

Expected: 👍 accept · Size: 813 B · Lines: 16 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.1 MB

stderr:

checked in 0.000369s

Test "tutorial/020_imax2"

Expected: 👍 accept · Size: 832 B · Lines: 17 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.2 MB

stderr:

checked in 0.000363s

Test "tutorial/021_inferVar"

Expected: 👍 accept · Size: 717 B · Lines: 12 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.1 MB

stderr:

checked in 0.000292s

Test "tutorial/022_defEqLambda"

Expected: 👍 accept · Size: 1.4 KB · Lines: 26 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000362s

Test "tutorial/023_peano1"

Expected: 👍 accept · Size: 3.6 KB · Lines: 73 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.2 MB

stderr:

checked in 0.000454s

Test "tutorial/024_peano2"

Expected: 👍 accept · Size: 4.5 KB · Lines: 90 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.4 MB

stderr:

checked in 0.000535s

Test "tutorial/025_peano3"

Expected: 👍 accept · Size: 4.9 KB · Lines: 98 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.4 M · max rss memory: 7.4 MB

stderr:

checked in 0.000571s

Test "tutorial/026_letType"

Expected: 👍 accept · Size: 493 B · Lines: 9 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.1 MB

stderr:

checked in 0.000305s

Test "tutorial/027_letTypeDep"

Expected: 👍 accept · Size: 1.2 KB · Lines: 26 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.2 MB

stderr:

checked in 0.000355s

Test "tutorial/028_letRed"

Expected: 👍 accept · Size: 631 B · Lines: 12 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.1 MB

stderr:

checked in 0.000325s

Test "tutorial/029_empty"

Expected: 👍 accept · Size: 1.2 KB · Lines: 20 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.1 MB

stderr:

checked in 0.000369s

Test "tutorial/030_boolType"

Expected: 👍 accept · Size: 2.3 KB · Lines: 37 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 17 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000375s

Test "tutorial/031_twoBool"

Expected: 👍 accept · Size: 4.2 KB · Lines: 65 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

checked in 0.000408s

Test "tutorial/032_andType"

Expected: 👍 accept · Size: 3.2 KB · Lines: 57 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000372s

Test "tutorial/033_prodType"

Expected: 👍 accept · Size: 3.8 KB · Lines: 76 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

checked in 0.000412s

Test "tutorial/034_pprodType"

Expected: 👍 accept · Size: 3.8 KB · Lines: 75 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.2 MB

stderr:

checked in 0.000382s

Test "tutorial/035_pUnitType"

Expected: 👍 accept · Size: 1.8 KB · Lines: 31 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.2 MB

stderr:

checked in 0.000347s

Test "tutorial/036_eqType"

Expected: 👍 accept · Size: 3.2 KB · Lines: 62 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 7 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

checked in 0.000458s

Test "tutorial/037_natDef"

Expected: 👍 accept · Size: 3.3 KB · Lines: 61 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

checked in 0.000401s

Test "tutorial/038_rbTreeDef"

Expected: 👍 accept · Size: 15.7 KB · Lines: 296 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.5 M · max rss memory: 7.4 MB

stderr:

checked in 0.000580s

Test "tutorial/039_inductBadNonSort"

Expected: ✋ reject · Size: 1.2 KB · Lines: 20 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

inductive inductBadNonSort : constType
                             ^^^^^^^^^
                             has type
                               Type → Type → Type
                             but is expected to be a Sort (Type or Prop)
checked in 0.000427s

Test "tutorial/040_inductBadNonSort2"

Expected: ✋ reject · Size: 602 B · Lines: 8 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.1 MB

stderr:

inductive inductBadNonSort2 : aType
                              ^^^^^
                              has type
                                Type
                              but is expected to be a Sort (Type or Prop)
checked in 0.000339s

Test "tutorial/041_inductLevelParam"

Expected: ✋ reject · Size: 519 B · Lines: 7 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 6.9 MB

stderr:

Invalid declaration inductLevelParam.{u, u}: duplicate level parameter u

checked in 0.000298s

Test "tutorial/042_inductTooFewParams"

Expected: ✋ reject · Size: 552 B · Lines: 6 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 7.0 MB

stderr:

inductive inductTooFewParams : Prop → Prop
                               ^^^^^^^^^^^
                               has type
                                 Prop
                               but is expected to be a Sort (Type or Prop)
checked in 0.000294s

Test "tutorial/043_inductWrongCtorParams"

Expected: ✋ reject · Size: 1.2 KB · Lines: 16 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.1 MB

stderr:

inductive inductWrongCtorParams : Prop → Type
| mk : Type → inductWrongCtorParams aProp
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       invalid return type
checked in 0.000432s

Test "tutorial/044_inductWrongCtorResParams"

Expected: ✋ reject · Size: 1.3 KB · Lines: 19 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

inductive inductWrongCtorResParams : Prop → Prop → Type
| mk : (x : Prop) → (y : Prop) → inductWrongCtorResParams y x
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       invalid return type
checked in 0.000397s

Test "tutorial/045_inductWrongCtorResLevel"

Expected: ✋ reject · Size: 1.4 KB · Lines: 23 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

inductive inductWrongCtorResLevel.{u1, u2} : Prop → Prop → Type
| mk : (x : Prop) → (y : Prop) → inductWrongCtorResLevel.{u2, u1} x y
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       invalid return type
checked in 0.000392s

Test "tutorial/046_inductInIndex"

Expected: ✋ reject · Size: 1.1 KB · Lines: 14 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.1 MB

stderr:

inductive inductInIndex : Prop → Prop
| mk : inductInIndex (inductInIndex aProp)
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       invalid return type
checked in 0.000354s

Test "tutorial/047_indNeg"

Expected: ✋ reject · Size: 1000 B · Lines: 12 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

inductive indNeg : Type
| mk : (indNeg → indNeg) → indNeg
        ^^^^^^^^^^^^^^^
        arg #1 has a non-positive occurrence of the datatype being declared
checked in 0.000333s

Test "tutorial/048_reduceCtorParam.mk"

Expected: 👍 accept · Size: 4.1 KB · Lines: 80 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.2 MB

stderr:

checked in 0.000483s

Test "tutorial/049_reduceCtorType.mk"

Expected: ✋ reject · Size: 1.5 KB · Lines: 26 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

inductive reduceCtorType : Type
| mk : id reduceCtorType
       ^^^^^^^^^^^^^^^^^
       invalid return type
checked in 0.000420s

Test "tutorial/050_indNegReducible"

Expected: ✋ reject · Size: 1.9 KB · Lines: 31 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

inductive indNegReducible : Type
| mk : (constType aType indNegReducible → indNegReducible) → indNegReducible
        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
        arg #1 has a non-positive occurrence of the datatype being declared
checked in 0.000431s

Test "tutorial/051_predWithTypeField"

Expected: 👍 accept · Size: 2.0 KB · Lines: 32 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000341s

Test "tutorial/052_typeWithTypeField"

Expected: 👍 accept · Size: 2.1 KB · Lines: 36 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000386s

Test "tutorial/053_typeWithTypeFieldPoly"

Expected: 👍 accept · Size: 2.1 KB · Lines: 38 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000356s

Test "tutorial/054_typeWithTooHighTypeField.mk"

Expected: ✋ reject · Size: 947 B · Lines: 11 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.1 MB

stderr:

inductive typeWithTooHighTypeField : Type
| mk : Type → typeWithTooHighTypeField
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       has field of type
         Type
       at universe level 2, but the inductive is at universe level 1
checked in 0.000352s

Test "tutorial/055_emptyRec"

Expected: 👍 accept · Size: 1.2 KB · Lines: 21 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000433s

Test "tutorial/056_boolRec"

Expected: 👍 accept · Size: 3.0 KB · Lines: 53 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

checked in 0.000413s

Test "tutorial/057_twoBoolRec"

Expected: 👍 accept · Size: 4.8 KB · Lines: 78 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.2 MB

stderr:

checked in 0.000445s

Test "tutorial/058_andRec"

Expected: 👍 accept · Size: 3.2 KB · Lines: 58 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

checked in 0.000446s

Test "tutorial/059_prodRec"

Expected: 👍 accept · Size: 4.0 KB · Lines: 79 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.2 MB

stderr:

checked in 0.000469s

Test "tutorial/060_pprodRec"

Expected: 👍 accept · Size: 4.0 KB · Lines: 78 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.2 MB

stderr:

checked in 0.000465s

Test "tutorial/061_punitRec"

Expected: 👍 accept · Size: 2.2 KB · Lines: 39 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

checked in 0.000390s

Test "tutorial/062_eqRec"

Expected: 👍 accept · Size: 3.3 KB · Lines: 63 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.2 MB

stderr:

checked in 0.000382s

Test "tutorial/063_nRec"

Expected: 👍 accept · Size: 3.3 KB · Lines: 61 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

checked in 0.000378s

Test "tutorial/064_rbTreeRef"

Expected: 👍 accept · Size: 16.2 KB · Lines: 303 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 18 ms · instructions: 13.1 M · max rss memory: 7.5 MB

stderr:

checked in 0.000720s

Test "tutorial/065_boolPropRec"

Expected: 👍 accept · Size: 2.3 KB · Lines: 34 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000418s

Test "tutorial/066_existsRec"

Expected: 👍 accept · Size: 3.6 KB · Lines: 66 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.2 MB

stderr:

checked in 0.000406s

Test "tutorial/067_sortElimPropRec"

Expected: 👍 accept · Size: 5.6 KB · Lines: 97 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.2 MB

stderr:

checked in 0.000427s

Test "tutorial/068_sortElimProp2Rec"

Expected: 👍 accept · Size: 6.6 KB · Lines: 114 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.4 MB

stderr:

checked in 0.000526s

Test "tutorial/069_boolRecEqns"

Expected: 👍 accept · Size: 10.8 KB · Lines: 199 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.8 M · max rss memory: 7.5 MB

stderr:

checked in 0.000673s

Test "tutorial/070_prodRecEqns"

Expected: 👍 accept · Size: 10.1 KB · Lines: 205 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 13.2 M · max rss memory: 7.6 MB

stderr:

checked in 0.000732s

Test "tutorial/071_nRecReduction"

Expected: 👍 accept · Size: 12.7 KB · Lines: 238 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 13.0 M · max rss memory: 7.5 MB

stderr:

checked in 0.000727s

Test "tutorial/072_listRecReduction"

Expected: 👍 accept · Size: 17.5 KB · Lines: 335 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 7 ms · instructions: 15.0 M · max rss memory: 8.0 MB

stderr:

checked in 0.001124s

Test "tutorial/073_RBTree.id_spec"

Expected: 👍 accept · Size: 47.9 KB · Lines: 1.0 k · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 14 ms · instructions: 33.8 M · max rss memory: 14.2 MB

stderr:

checked in 0.008306s

Test "tutorial/074_And.right"

Expected: 👍 accept · Size: 4.3 KB · Lines: 74 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.2 MB

stderr:

checked in 0.000423s

Test "tutorial/075_Prod.snd"

Expected: 👍 accept · Size: 4.5 KB · Lines: 83 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.2 MB

stderr:

checked in 0.000457s

Test "tutorial/076_PProd.snd"

Expected: 👍 accept · Size: 4.5 KB · Lines: 83 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.2 MB

stderr:

checked in 0.000442s

Test "tutorial/077_PSigma.snd"

Expected: 👍 accept · Size: 5.1 KB · Lines: 96 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.4 MB

stderr:

checked in 0.000467s

Test "tutorial/078_projOutOfRange"

Expected: ✋ reject · Size: 3.8 KB · Lines: 67 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.2 MB

stderr:

def projOutOfRange : ∀ (x : Prop), ∀ (x : Prop), And x x → x :=
  fun x y z ↦ z.2
  ^^^^^^^^^^^^^^^
  invalid projection And.2: And has only 2 fields
checked in 0.000461s

Test "tutorial/079_projNotStruct"

Expected: ✋ reject · Size: 3.5 KB · Lines: 64 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

def projNotStruct : N → N :=
  fun x ↦ x.0
          ^^^
          N is not a structure (it has 2 constructors)
checked in 0.000391s

Test "tutorial/080_projProp1"

Expected: 👍 accept · Size: 8.2 KB · Lines: 143 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.2 MB

stderr:

checked in 0.000469s

Test "tutorial/081_projProp2"

Expected: ✋ reject · Size: 8.2 KB · Lines: 143 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.2 MB

stderr:

def projProp2 : PropStructure.{0, 1} → PUnit.{1} :=
  fun x ↦ x.someData
          ^^^^^^^^^^
          cannot project a non-propositional field from a propositional structure
checked in 0.000518s

Test "tutorial/082_projProp3"

Expected: 👍 accept · Size: 8.2 KB · Lines: 143 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.2 MB

stderr:

checked in 0.000465s

Test "tutorial/083_projProp4"

Expected: ✋ reject · Size: 8.2 KB · Lines: 143 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.2 MB

stderr:

def projProp4 : PropStructure.{0, 1} → PUnit.{1} :=
  fun x ↦ x.someMoreData
          ^^^^^^^^^^^^^^
          cannot project a non-propositional field from a propositional structure
checked in 0.000604s

Test "tutorial/084_projProp5"

Expected: ✋ reject · Size: 8.4 KB · Lines: 148 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.2 MB

stderr:

def projProp5 : ∀ (x : PropStructure.{0, 1}), Eq x.someMoreData x.someMoreData :=
                                                 ^^^^^^^^^^^^^^
                                                 cannot project a non-propositional field from a propositional structure
checked in 0.000554s

Test "tutorial/085_projProp6"

Expected: ✋ reject · Size: 8.2 KB · Lines: 143 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.2 MB

stderr:

def projProp6 : PropStructure.{0, 1} → PUnit.{0} :=
  fun x ↦ x.aFinalProof
          ^^^^^^^^^^^^^
          cannot project a non-propositional field from a propositional structure
checked in 0.000487s

Test "tutorial/086_projDataIndexRec"

Expected: 👍 accept · Size: 6.8 KB · Lines: 111 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.2 MB

stderr:

checked in 0.000446s

Test "tutorial/087_projIndexData"

Expected: ✋ reject · Size: 6.8 KB · Lines: 111 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.2 MB

stderr:

def projIndexData : (x : N) → ProjDataIndex x → N :=
  fun x x ↦ x.0
  ^^^^^^^^^^^^^
  invalid projection PropStructure.0: unknown structure PropStructure
checked in 0.000484s

Test "tutorial/088_projIndexData2"

Expected: ✋ reject · Size: 6.8 KB · Lines: 111 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.2 MB

stderr:

def projIndexData2 : ∀ (x : N), ProjDataIndex x → True :=
  fun x x ↦ x.1
  ^^^^^^^^^^^^^
  invalid projection PropStructure.1: unknown structure PropStructure
checked in 0.000448s

Test "tutorial/089_projRed"

Expected: 👍 accept · Size: 9.9 KB · Lines: 177 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.4 MB

stderr:

checked in 0.000538s

Test "tutorial/090_ruleK"

Expected: 👍 accept · Size: 6.5 KB · Lines: 121 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.2 MB

stderr:

checked in 0.000466s

Test "tutorial/091_ruleKbad"

Expected: ✋ reject · Size: 6.5 KB · Lines: 121 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.4 MB

stderr:

theorem ruleKbad : ∀ (h : Eq Bool.true Bool.false), ∀ (a : Bool), Eq (Eq.rec a h) a := fun x a ↦ Eq.refl a
                                                                                       ^^^^^^^^^^^^^^^^^^^
                                                                                       has type
                                                                                         Eq Bool.true Bool.false → ∀ (a : Bool), Eq a a
                                                                                       but is expected to have type
                                                                                         ∀ (h : Eq Bool.true Bool.false), ∀ (a : Bool), Eq (Eq.rec a h) a
checked in 0.000561s

Test "tutorial/092_ruleKAcc"

Expected: ✋ reject · Size: 12.8 KB · Lines: 238 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 13.9 M · max rss memory: 7.8 MB

stderr:

theorem ruleKAcc.{u} : ∀ (α : Sort u), ∀ (p : ∀ (a : α), ∀ (a : α), Prop), ∀ (x : α), ∀ (h : Acc p x), ∀ (a : Bool), Eq (Acc.rec (fun x x x ↦ a) h) a := fun α p x h a ↦ Eq.refl a
                                                                                                                                                         ^^^^^^^^^^^^^^^^^^^^^^^^^
                                                                                                                                                         has type
                                                                                                                                                           ∀ (α : Sort u), ∀ (p : ∀ (a : α), ∀ (a : α), Prop), ∀ (x : α), Acc p x → ∀ (a : Bool), Eq a a
                                                                                                                                                         but is expected to have type
                                                                                                                                                           ∀ (α : Sort u), ∀ (p : ∀ (a : α), ∀ (a : α), Prop), ∀ (x : α), ∀ (h : Acc p x), ∀ (a : Bool), Eq (Acc.rec (fun x x x ↦ a) h) a
checked in 0.000890s

Test "tutorial/093_aNatLit"

Expected: 👍 accept · Size: 3.0 KB · Lines: 54 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:

checked in 0.000324s

Test "tutorial/094_natLitEq"

Expected: 👍 accept · Size: 6.1 KB · Lines: 114 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.2 MB

stderr:

checked in 0.000436s

Test "tutorial/095_proofIrrelevance"

Expected: 👍 accept · Size: 5.0 KB · Lines: 100 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.2 MB

stderr:

checked in 0.000433s

Test "tutorial/096_unitEta1"

Expected: 👍 accept · Size: 6.2 KB · Lines: 116 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 14 ms · instructions: 12.0 M · max rss memory: 7.2 MB

stderr:

checked in 0.000455s

Test "tutorial/097_unitEta2"

Expected: 👍 accept · Size: 6.0 KB · Lines: 109 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.2 MB

stderr:

checked in 0.000412s

Test "tutorial/098_unitEta3"

Expected: 👍 accept · Size: 6.0 KB · Lines: 111 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.2 MB

stderr:

checked in 0.000415s

Test "tutorial/099_structEta"

Expected: 👍 accept · Size: 12.5 KB · Lines: 230 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 13.1 M · max rss memory: 7.5 MB

stderr:

checked in 0.000668s

Test "tutorial/100_funEta"

Expected: 👍 accept · Size: 5.2 KB · Lines: 104 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.2 MB

stderr:

checked in 0.000512s

Test "tutorial/101_funEtaDep"

Expected: 👍 accept · Size: 5.3 KB · Lines: 106 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.4 MB

stderr:

checked in 0.000464s

Test "tutorial/102_funEtaBad"

Expected: ✋ reject · Size: 4.9 KB · Lines: 97 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.4 MB

stderr:

theorem funEtaBad : ∀ (α : Type), ∀ (β : Type), ∀ (g : α → α), ∀ (f : α → β), Eq (fun x ↦ f (g x)) f := fun x x x f ↦ Eq.refl f
                                                                                                        ^^^^^^^^^^^^^^^^^^^^^^^
                                                                                                        has type
                                                                                                          ∀ (x : Type), ∀ (x : Type), ∀ (x : x → x), ∀ (f : x → x), Eq f f
                                                                                                        but is expected to have type
                                                                                                          ∀ (α : Type), ∀ (β : Type), ∀ (g : α → α), ∀ (f : α → β), Eq (fun x ↦ f (g x)) f
checked in 0.000627s

Test "tutorial/103_etaRuleK"

Expected: ✋ reject · Size: 6.5 KB · Lines: 121 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.4 MB

stderr:

def etaRuleK : ∀ (a : Eq Bool.true Bool.true → Bool), Eq (Eq.rec (a (Eq.refl Bool.true))) a :=
  fun a ↦ Eq.refl a
  ^^^^^^^^^^^^^^^^^
  has type
    ∀ (a : Eq Bool.true Bool.true → Bool), Eq a a
  but is expected to have type
    ∀ (a : Eq Bool.true Bool.true → Bool), Eq (Eq.rec (a (Eq.refl Bool.true))) a
checked in 0.000556s

Test "tutorial/104_etaCtor"

Expected: ✋ reject · Size: 9.0 KB · Lines: 148 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.4 MB

stderr:

def etaCtor : ∀ (x : True → T), Eq (T.mk (T.val (x True.intro))) x :=
  fun x ↦ Eq.refl x
  ^^^^^^^^^^^^^^^^^
  has type
    ∀ (x : True → T), Eq x x
  but is expected to have type
    ∀ (x : True → T), Eq (T.mk (T.val (x True.intro))) x
checked in 0.000565s

Test "tutorial/105_reflOccLeft"

Expected: ✋ reject · Size: 3.7 KB · Lines: 61 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.2 MB

stderr:

inductive reflOccLeft : Type
| mk : (Nat → reflOccLeft → Nat) → reflOccLeft
        ^^^^^^^^^^^^^^^^^^^^^^^
        arg #1 has a non-positive occurrence of the datatype being declared
checked in 0.000383s

Test "tutorial/106_reflOccInIndex"

Expected: ✋ reject · Size: 4.0 KB · Lines: 66 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.2 MB

stderr:

inductive reflOccInIndex : Type → Type
| mk : (α : Type) → ((x : Nat) → reflOccInIndex (reflOccInIndex x)) → reflOccInIndex α
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       constructor declares 1 field but type has 2
checked in 0.000432s

Test "tutorial/107_reduceCtorParamRefl.mk"

Expected: 👍 accept · Size: 4.5 KB · Lines: 88 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.2 MB

stderr:

checked in 0.000427s

Test "tutorial/108_reduceCtorParamRefl2.mk"

Expected: 👍 accept · Size: 4.5 KB · Lines: 88 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.2 MB

stderr:

checked in 0.000446s

Test "tutorial/109_rTreeRec"

Expected: 👍 accept · Size: 5.5 KB · Lines: 91 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.2 MB

stderr:

checked in 0.000477s

Test "tutorial/110_rtreeRecReduction"

Expected: 👍 accept · Size: 10.8 KB · Lines: 193 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.6 M · max rss memory: 7.4 MB

stderr:

checked in 0.000686s

Test "tutorial/111_accRecType"

Expected: 👍 accept · Size: 7.5 KB · Lines: 151 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.4 MB

stderr:

checked in 0.000497s

Test "tutorial/112_accRecReduction"

Expected: 👍 accept · Size: 13.4 KB · Lines: 252 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 7 ms · instructions: 14.4 M · max rss memory: 7.9 MB

stderr:

checked in 0.001015s

Test "tutorial/113_accRecNoEta"

Expected: ✋ reject · Size: 13.0 KB · Lines: 244 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 13.9 M · max rss memory: 7.8 MB

stderr:

theorem accRecNoEta : ∀ {α : Type}, ∀ (r : ∀ (a : α), ∀ (a : α), Prop), ∀ (a : α), ∀ (h : Acc r a), ∀ (p : Bool), Eq (Acc.rec (fun x x x ↦ p) h) p := fun α r a h p ↦ Eq.refl p
                                                                                                                                                      ^^^^^^^^^^^^^^^^^^^^^^^^^
                                                                                                                                                      has type
                                                                                                                                                        ∀ (α : Type), ∀ (r : ∀ (a : α), ∀ (a : α), Prop), ∀ (a : α), Acc r a → ∀ (p : Bool), Eq p p
                                                                                                                                                      but is expected to have type
                                                                                                                                                        ∀ {α : Type}, ∀ (r : ∀ (a : α), ∀ (a : α), Prop), ∀ (a : α), ∀ (h : Acc r a), ∀ (p : Bool), Eq (Acc.rec (fun x x x ↦ p) h) p
checked in 0.000899s

Test "tutorial/114_quotMkType"

Expected: 👍 accept · Size: 6.3 KB · Lines: 123 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.2 MB

stderr:

checked in 0.000526s

Test "tutorial/115_quotIndType"

Expected: 👍 accept · Size: 6.3 KB · Lines: 124 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.2 MB

stderr:

checked in 0.000456s

Test "tutorial/116_quotLiftType"

Expected: 👍 accept · Size: 6.3 KB · Lines: 124 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.2 MB

stderr:

checked in 0.000512s

Test "tutorial/117_quotSoundType"

Expected: 👍 accept · Size: 7.2 KB · Lines: 141 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.4 MB

stderr:

checked in 0.000542s

Test "tutorial/118_quotLiftReduction"

Expected: 👍 accept · Size: 7.8 KB · Lines: 153 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.8 M · max rss memory: 7.5 MB

stderr:

checked in 0.000724s

Test "tutorial/119_quotIndReduction"

Expected: 👍 accept · Size: 7.6 KB · Lines: 151 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.7 M · max rss memory: 7.5 MB

stderr:

checked in 0.000656s

Test "tutorial/120_dup_defs"

Expected: ✋ reject · Size: 479 B · Lines: 7 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.1 MB

stderr:

Invalid declaration dup_defs: already declared as def dup_defs : Type :=
  Prop

checked in 0.000336s

Test "tutorial/121_dup_ind_def"

Expected: ✋ reject · Size: 1.7 KB · Lines: 27 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.0 MB

stderr:

expected name index 4, got 8

checked in 0.000306s

Test "tutorial/122_dup_ctor_def"

Expected: ✋ reject · Size: 1.7 KB · Lines: 27 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 7.0 MB

stderr:

expected name index 4, got 8

checked in 0.000298s

Test "tutorial/123_dup_rec_def"

Expected: ✋ reject · Size: 1.7 KB · Lines: 27 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.0 MB

stderr:

expected name index 4, got 8

checked in 0.000329s

Test "tutorial/124_dup_rec_def2"

Expected: ✋ reject · Size: 1.7 KB · Lines: 28 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 7.0 MB

stderr:

expected name index 5, got 9

checked in 0.000339s

Test "tutorial/125_dup_ctor_rec"

Expected: ✋ reject · Size: 1.5 KB · Lines: 24 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 6.9 MB

stderr:

expected name index 3, got 6

checked in 0.000304s

Test "tutorial/126_DupConCon"

Expected: ✋ reject · Size: 2.2 KB · Lines: 35 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.4 M · max rss memory: 6.9 MB

stderr:

expected name index 4, got 7

checked in 0.000348s