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Require Import Setoid.
Parameter recursion : forall A : Set, A -> (nat -> A -> A) -> nat -> A.
Axiom recursion_S :
forall (A : Set) (EA : relation A) (a : A) (f : nat -> A -> A) (n : nat),
EA (recursion A a f (S n)) (f n (recursion A a f n)).
Goal forall n : nat, recursion nat 0 (fun _ _ => 1) (S n) = 1.
intro n.
rewrite recursion_S.
reflexivity.
Qed.
Goal forall n : nat, recursion nat 0 (fun _ _ => 1) (S n) = 1.
intro n.
setoid_rewrite recursion_S.
reflexivity.
Qed.
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