(** ** Parity *)

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

Lemma sqrt_iter_spec : forall k p q r, q = p+p -> r<=q -> let s := sqrt_iter k p q r in s*s <= k + p*p + (q - r) < (S s)*(S s).