Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
fa449aab14
This PR introduces a `mutual_induct` variant of the generated (co)induction proof principle for mutually defined (co)inductive predicates. Unlike the standard (co)induction principle (which projects conclusions separately for each predicate), `mutual_induct` produces a conjunction of all conclusions. ## Example Given the following mutual definition: ```lean4 mutual def f : Prop := g coinductive_fixpoint def g : Prop := f coinductive_fixpoint end ``` Standard coinduction principles: ```lean4 f.coind : ∀ (pred_1 pred_2 : Prop), (pred_1 → pred_2) → (pred_2 → pred_1) → pred_1 → f g.coind : ∀ (pred_1 pred_2 : Prop), (pred_1 → pred_2) → (pred_2 → pred_1) → pred_2 → g ``` New `mutual_induct`principle: ```lean4 f.mutual_induct: ∀ (pred_1 pred_2 : Prop), (pred_1 → pred_2) → (pred_2 → pred_1) → (pred_1 → f) ∧ (pred_2 → g) ``` --------- Co-authored-by: Joachim Breitner <mail@joachim-breitner.de> |
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