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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. \ No newline at end of file