Local Hint Resolve lt_p_w le_p_w le_0_wmp : a.

(* <KEEP TOGETHER - s'_eq *)
Lemma s'_eq : _Z s' = x mod 2 ^ w - x mod 2 ^ p.
unfold s'. rewrite Z_from_multp2. fold p. rewrite s_eq. rewrite Zmult_comm. rewrite modred.