Lean Kernel Arena / bugs/nested-unused-param

Checks that the parameters of a nested inductive application are type-checked even when they do not appear in the auxiliary type generated during nested-inductive compilation.

When an inductive E has a constructor whose type contains a nested application L (E w) b, the elaboration of nested inductives replaces that occurrence with an auxiliary type. The argument b does not occur in the auxiliary declaration, so a checker that only checks the auxiliary type never sees b. A correct checker must still ensure b is well-typed; this test rejects if it is not.

Here b is a malformed projection C.0 (C.0 w) (applying a C projection to a value of the unrelated structure W), disguised by a hash collision. If the parameter is not checked, the bogus projection slips through and the resulting E can be used to build an axiom-free proof of False (boom). The projection is merely the payload; the property under test is that the nested-inductive parameter is checked.

Origin: reported as leanprover/lean4#14576 by @kiranandcode, with the original source recorded by @xrchz (https://github.com/xrchz/collatzlean); fixed in leanprover/lean4#14577.