rewrite <- Zpower_exp. replace (w - p + p) with w. trivial. ring. cut (p < w). omega. auto with a. apply Zle_ge. auto with a.
Qed.

Lemma mod2p : forall a b c', (a * 2 ^ w + b) mod 2 ^ p = (c' * 2 ^ w + b) mod 2 ^ p.
clear x_i_in_Z_ x_i s_i s'_i s''_i h'_i q_i q'_i y_i h'_i h'_i' x'.