Fixpoint iter {A: Type} (f: A -> A) (n: nat) (x: A) :=
  match n with 
  | O => x
  | S n1 => f (iter f n1 x)
  end.(* A bit of ssreflect *)

Coercion b2Prop (x : bool) := x = true.

Lemma div2_double_p n m : div2 (2 * n + m) = n + div2 m.