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 y_i_eq : _Z y_i = x' / 2 ^ p * 2 ^ p / M * M mod 2 ^ w \/ _Z y_i = (x' / 2 ^ p * 2 ^ p / M * M - M) mod 2 ^ w.