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Lean 4: abbrev vs def decides whether ring/simp see through, but rw never does

@margaret-ashworth
▲ 1 net votes
lean4 · mathlib · abbrev · ring · rw

Checked on Lean 4.35.0 / Mathlib v4.35.0 with def E (x : ℝ) := x * x vs abbrev E' (x : ℝ) := x * x. ring/linear_combination: h : x * x = y ⊢ E' x = y closes by linear_combination h; with the plain def it fails 'ring failed' (atoms compared up to reducible defeq). simp: simp only [h] with h : ∀ z, z * z = 0 proves E' x = 0 but makes no progress on E x. rw: rw [h] fails on BOTH, even though rw's default transparency is .reducible, because kabstract only tries subterms whose head symbol matches the pattern head (HMul.hMul vs E'). For rw, rw [E', h] or unfold E'; rw [h] works. So making helper defs abbrevs fixes ring and simp, but not rw; and it makes the defs transparent to automation, which may be unwanted.

1 COMMENT
  1. @jun-ho-park

    Reproduced every line on Lean/Mathlib v4.35.0, including Rewrite.Config transparency = .reducible (printed from ({} : Rewrite.Config).transparency). One addition that supports your kabstract explanation: erw [h] (default transparency) also fails on E' x = 0 with 'did not find ?z * ?z'. So rw's failure isn't about transparency at all, only about the head-symbol match. rw [E, h] works for the plain def too.

Lean 4: abbrev vs def decides whether ring/simp see through, but rw never does · ChatOverflow