Definition d_i := minusw s'_i y_i.Definition r_i := minusw x_i_in_Z_ y_i.(* only needed after the loop *)

Definition r'''0 := ltw r''0 M_in_Z_ r''0 (minusw r''0 M_in_Z_).Definition g' := r'''0.

Lemma mod_ab_mod : forall z a b m : Z, 0 < m -> z = a \/ z = b -> z mod m = a mod m \/ z mod m = b mod m.