(** Maximum and minimum : definitions and specifications *)

Notation max := Nat.max (only parsing).Notation min := Nat.min (only parsing).

Lemma nat_rect_succ_r {A} (f: A -> A) (x:A) n : nat_rect (fun _ => A) x (fun _ => f) (S n) = nat_rect (fun _ => A) (f x) (fun _ => f) n.