3d1d8fc1de
This PR adds the “unfolding” variant of the functional induction and functional cases principles, under the name `foo.induct_unfolding` resp. `foo.fun_cases_unfolding`. These theorems combine induction over the structure of a recursive function with the unfolding of that function, and should be more reliable, easier to use and more efficient than just case-splitting and then rewriting with equational theorems. For example instead of ``` ackermann.induct (motive : Nat → Nat → Prop) (case1 : ∀ (m : Nat), motive 0 m) (case2 : ∀ (n : Nat), motive n 1 → motive (Nat.succ n) 0) (case3 : ∀ (n m : Nat), motive (n + 1) m → motive n (ackermann (n + 1) m) → motive (Nat.succ n) (Nat.succ m)) (x x : Nat) : motive x x ``` one gets ``` ackermann.fun_cases_unfolding (motive : Nat → Nat → Nat → Prop) (case1 : ∀ (m : Nat), motive 0 m (m + 1)) (case2 : ∀ (n : Nat), motive n.succ 0 (ackermann n 1)) (case3 : ∀ (n m : Nat), motive n.succ m.succ (ackermann n (ackermann (n + 1) m))) (x✝ x✝¹ : Nat) : motive x✝ x✝¹ (ackermann x✝ x✝¹) ``` |
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