This PR fixes a regression introduced in Lean 4.29.0-rc2 where `simp` no
longer simplifies inside type class instance arguments due to the
`backward.isDefEq.respectTransparency` change. This breaks proofs where
a term like `(a :: l).length` appears both in the main expression and
inside implicit instance arguments (e.g., determining a `BitVec` width).
**The problem:** After `simp only [List.length_cons]`, the main
expression has `l.length + 1` but instances still have `(a ::
l).length`. Since `simp` no longer simplifies inside instances, and
`isDefEq` won't unfold `List.length` at the default transparency,
subsequent lemma applications fail.
**Reproducer** (from Son Ho, reported by Sebastian Ullrich):
```lean
theorem BitVec.getElem!_eq_testBit_toNat {w : Nat} (x : BitVec w) (i : Nat) :
x[i]! = x.toNat.testBit i := by sorry
example (l : List Nat) (a : Nat) (j : Nat) :
(0#((a :: l).length))[j]! = (0#((a :: l).length)).toNat.testBit j := by
simp only [List.length_cons]
simp only [BitVec.getElem!_eq_testBit_toNat] -- works in 4.28.0-rc1, fails in 4.29.0-rc6
```
**The fix:** Mark `List.length` as `@[implicit_reducible]`, allowing
`isDefEq` to unfold it when checking implicit arguments. Several proofs
that previously needed a trailing `rfl` after `simp` now close directly,
since `simp` can see through `List.length` in more positions.
**Longer term:** The root cause is that `GetElem` carries complex proof
obligations in its type class instances, making implicit arguments
sensitive to definitional equality of collection sizes. We are
considering a redesign with a noncomputable `GetElemV` variant based on
`Nonempty` that avoids these casts entirely, but that is a larger change
planned for a future release.
---------
Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>
