intros z a b m H H0. elim H0; intro H1; rewrite H1; tauto. Qed.

(* <KEEP TOGETHER - q'_eq *)
Lemma q'_eq :
_Z q' = (x / 2 ^ p * 2 ^ p / M) mod 2 ^ w \/
_Z q' = (x / 2 ^ p * 2 ^ p / M - 1) mod 2 ^ w.