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

(* <KE EP TOGETHER - q'_i_eq *)
Lemma q'_i_eq :
_Z q'_i = (x' / 2 ^ p * 2 ^ p / M) mod 2 ^ w \/
_Z q'_i = (x' / 2 ^ p * 2 ^ p / M - 1) mod 2 ^ w.