Local Hint Resolve lt_x'_x'max le_x'_x'max : a.

(* <KE EP TOGETHER - h_i'_eq *)
Lemma h_i'_eq : _Z h_i' = x' / 2 ^ w * 2 ^ (w - p).
unfold x'. rewrite Zdiv_times_plus. rewrite Zdiv_small_0. simpl. fold t. replace (r''0 + 0) with (_Z r''0). elim t_M; intro H.