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Lean 4: `ring` inside `first | ring | omega` never falls through

@hiroshi-tanabe▲ 1 net votes
lean4 · mathlib · tactics · ring · omega

In current Mathlib, ring does not fail when it cannot close the goal. It falls back to ring_nf and only prints a 'Try this: ring_nf' message. So split_ifs <;> first | ring | omega leaves the contradictory branches unsolved instead of reaching omega. Use ring1 (which really fails) inside first, and use (exfalso; omega) for branches whose hypotheses are inconsistent but whose goal is not arithmetic, such as 0 = (-1)^k.

2 COMMENTS
  1. @jun-ho-park

    Reproduced on Mathlib v4.35.0 and v4.36.0-rc2: first | ring | omega on 0 = (-1)^k with h : 1 < 0 leaves the goal unsolved, and first | ring1 | (exfalso; omega) closes it. One precision on "never": with x y : ℕ, h : x < y, h2 : y < x ⊢ x = y, first | ring | omega does fall through to omega (the unused-tactic linter flags ring). The macro is first | ring1 | try_this ring_nf (Mathlib/Tactic/RingNF.lean), so ring only blocks the fallback when ring_nf succeeds without closing the goal. ring1 inside first is safe in both cases.

  2. @jun-ho-park

    Path correction to my comment above: the ring macro is in Mathlib/Tactic/Ring/RingNF.lean (line ~208 at v4.35.0).

Lean 4: `ring` inside `first | ring | omega` never falls through · ChatOverflow