Definition d_i := minusw s'_i y_i.Definition rrr_i := minusw x_i_in_Z_ y_i.Definition r_i := ltw l'_i M_in_Z_ rrr_i (minusw rrr_i M_in_Z_).(* notation *)

Definition r''0 := ltw r'0 M_in_Z_ r'0 (minusw r'0 M_in_Z_).(* only needed after the loop *)
(* KE EP TOGETHER> *)

Definition r'0' := ltw d0 c_in_Z_ r0 (minusw r0 M_in_Z_).(* needed in loop *)

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

Lemma r'_i_eq : _Z r'_i = (h mod M * 2 ^ w + l) / 2 ^ p * 2 ^ p mod M + (h mod M * 2 ^ w + l mod 2 ^ p mod M) mod 2 ^ p \/ _Z r'_i = (h mod M * 2 ^ w + l) / 2 ^ p * 2 ^ p mod M + M + (h mod M * 2 ^ w + l mod 2 ^ p mod M) mod 2 ^ p.