(** Maximum and minimum : definitions and specifications *)
Notation max := Nat.max (only parsing).
Notation min := Nat.min (only parsing).

Theorem nat_rect_plus :
forall (n m:nat) {A} (f:A -> A) (x:A),
nat_rect (fun _ => A) x (fun _ => f) (n + m) =
nat_rect (fun _ => A) (nat_rect (fun _ => A) x (fun _ => f) m) (fun _ => f) n.