Lean Kernel Arena / nat-rec-rules

Proof of False via incorrect recursor rule validation.

When processing an inductive type declaration, a correct kernel must verify that the generated recursor rules match the ones provided in the export data. A checker that accidentally compares the imported rules against themselves (instead of against independently constructed rules) will accept arbitrary recursor reduction behavior.

This test defines Nat with a wrong Nat.rec succ rule that always returns hzero (ignoring the induction hypothesis). Combined with a nat literal extension that hardcodes correct arithmetic for concrete nat literals but falls back to the wrong Nat.rec rules for symbolic arguments, this creates an inconsistency that yields a proof of False.

Nanoda incorrectly accepted this proof until it was fixed.