(* KE EP TOGETHER> *)
unfold q_i. rewrite uhwm_eq. rewrite <- h'_i'h'_i_eq. rewrite h'_i'_eq. fold M'. rewrite M'_M. trivial. Qed.

Lemma q'_i_eq_pre :
_Z q'_i = (x' / 2 ^ p * (2 ^ (p + w) / M) / 2 ^ w) mod 2 ^ w.