Lean Kernel Arena / bugs/level-imax-leq

Test "bugs/level-imax-leq"

Expected: ✋ reject · Size: 5.6 KB · Lines: 93 · lean4export: 3.1.0 · Lean: 4.29.1 · 📄 Declaration

Proof of False via incorrect universe level comparison for imax.

A correct kernel must reject leq(imax(u,v)+1, imax(u,v)), since at u=0, v=0 this becomes leq(1, 0) which is false. However, a checker that only compares the imax arguments structurally (without accounting for an accumulated successor offset) will incorrectly accept it.

This allows defining a universe-collapsing identity function down.{u,v} : Sort (succ (imax u v)) → Sort (imax u v), which is used to cast between True and False via Bool.rec at Sort (imax 0 0) = Prop.

Nanoda incorrectly accepted this proof until it was fixed.

Checker Result ⏱️ 🧠
mathgraph ✋ 1 ms 29.8 MB
sokonanoda ✋ 1 ms 33.7 MB
nanoclo ✋ 1 ms 45.7 MB
con-ron ✋ 1 ms 12.1 MB
lazylean ✋ 1 ms 21.3 MB
nanoda ✋ 1 ms 3.1 MB
nanobruijn ✋ 1 ms 5.4 MB
con-leche ✋ 3 ms 17.7 MB
eink0rn ✋ 2 ms 11.6 MB
ind-models ✋ 58 ms 104.4 MB
official ✋ 28 ms 67.1 MB
lean4lean ✋ 74 ms 104.7 MB
tenet ✋ 134 ms 44.0 MB
nanoclo-fortran ✋ 1 ms 4.4 MB
lean4cobol ✋ 3 ms 13.4 MB
evmlean ✋ 687 ms 132.1 MB
mini ✋ 34 ms 73.4 MB
overfull ✋ 9.6 s 46.0 MB
kiota ✋ 1 ms 6.9 MB
canonical-min ✋ 387 ms 1.1 GB
rpylean ✋ 1 ms 4.3 MB
vow-lean-kernel ✋ 79 ms 8.3 MB
official-v4.28.0 ✋ 35 ms 74.4 MB
still-nanoda ✋ 1 ms 3.1 MB
nyaya ✋ 2 ms 9.2 MB
parse-only 👍 27 ms 65.4 MB