(** ** Parity *)

Definition Even n := exists m, n = 2*m.Definition Odd n := exists m, n = 2*m+1.

Lemma divmod_spec : forall x y q u, u <= y -> let (q',u') := divmod x y q u in x + (S y)*q + (y-u) = (S y)*q' + (y-u') /\ u' <= y.