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 sum_r'_i : forall a b : Z, (a mod M + b mod M) / M = 0 \/ (a mod M + b mod M) / M = 1.