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

Lemma RING_op_mult_l :
forall x y : R,
Equal (ring_mult (group_inverse R x) y) (group_inverse R (ring_mult x y)).