intros x; try assumption.
apply GROUP_reg_left with (module_mult (monoid_unit R) x); auto with algebra.
apply
Trans with (module_mult (sgroup_law R (monoid_unit R) (monoid_unit R)) x);
auto with algebra.
apply Trans with (module_mult (monoid_unit R) x); auto with algebra.
Qed.

Lemma MODULE_absorbant_r :
forall a : R, Equal (module_mult a (monoid_unit Mod)) (monoid_unit Mod).