Documentation

Lean.Meta.Tactic.Congr

Preprocessor before applying congruence theorem. Tries to close new goals using Eq.refl, HEq.refl, and assumption. It also tries to apply heq_of_eq.

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    Try to apply a simp congruence theorem.

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      Try to apply a hcongr congruence theorem, and then tries to close resulting goals using Eq.refl, HEq.refl, and assumption.

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        Try to apply implies_congr.

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          Given a goal of the form ⊢ f as = f bs, ⊢ (p → q) = (p' → q'), or HEq (f as) (f bs), try to apply congruence. It takes proof irrelevance into account, and the fact that Decidable p is a subsingleton.

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            def Lean.MVarId.congrN (mvarId : Lean.MVarId) (depth : optParam Nat 1000000) (closePre : optParam Bool true) (closePost : optParam Bool true) :

            Given a goal of the form ⊢ f as = f bs, ⊢ (p → q) = (p' → q'), or HEq (f as) (f bs), try to apply congruence. It takes proof irrelevance into account, and the fact that Decidable p is a subsingleton.

            • Applies congr recursively up to depth depth.
            • If closePre := true, it will attempt to close new goals using Eq.refl, HEq.refl, and assumption with reducible transparency.
            • If closePost := true, it will try again on goals on which congr failed to make progress with default transparency.
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            • mvarId.congrN depth closePre closePost = do let __discr(Lean.MVarId.congrN.go closePre closePost depth mvarId).run #[] match __discr with | (fst, s) => pure s.toList
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