Definition recursion {A} : A -> (N -> A -> A) -> N -> A :=
  peano_rect (fun _ => A).#[global]
Instance recursion_wd {A} (Aeq : relation A) :
 Proper (Aeq==>(Logic.eq==>Aeq==>Aeq)==>Logic.eq==>Aeq) recursion.

Lemma iter_swap_gen A B (f:A -> B) (g:A -> A) (h:B -> B) : (forall a, f (g a) = h (f a)) -> forall n a, f (iter n g a) = iter n h (f a).