intros x; try assumption.
apply GROUP_reg_right with (ring_mult x (monoid_unit R)).
apply Trans with (ring_mult x (sgroup_law R (monoid_unit R) (monoid_unit R)));
auto with algebra.
apply Trans with (ring_mult x (monoid_unit R)); auto with algebra.
Qed.
Hint Resolve RING_absorbant_r: algebra.

Lemma RING_absorbant_l :
forall x : R, Equal (ring_mult (monoid_unit R) x) (monoid_unit R).