induction passes wrong instance to function application

[llllvvuu]

Prerequisites

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Description

induction will use instances on the original variable in function applications on the new variable. The tactic will succeed, and indeed create new goals, but the proof will have a type error.

Context

This was discovered during usage of https://github.com/leanprover-community/repl, where we found a successful sequence of tactics resulting in an unsuccessful proof.

Steps to Reproduce

/--
warning: declaration uses 'sorry'
---
error: application type mismatch
  @Fin.instOfNat n inst✝
argument has type
  NeZero n✝
but function has type
  [inst : NeZero n] → {i : Nat} → OfNat (Fin n) i
-/
#guard_msgs in
example (n: Nat) [NeZero n] : (0 : Fin n) = 0 := by
  induction n <;> sorry

Expected behavior: An error on the tactic as it should try to synthesize NeZero 0 and NeZero n (where the original n is succ of this n) and both should fail.

Actual behavior: The tactic uses the original NeZero n✝ instance to synthesize Fin.instOfNat, for the new (0 : Fin n), which is not type-correct. Yet the tactic does not fail.

Versions

Lean 4.16.0-rc1
Target: x86_64-unknown-linux-gnu
live.lean-lang.org

Additional Information

Initially, #4246 looked similar, but I think it's not the same.

Impact

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[Kha]

Possible workaround/explainer what step is not happening: explicitly reverting the instance works

example (n: Nat) [inst : NeZero n] : (0 : Fin n) = 0 := by
  induction n generalizing inst <;> rfl