intros x y; try assumption.
apply Sym.
apply GROUP_law_inverse.
apply Trans with (ring_mult x (sgroup_law R y (group_inverse R y)));
auto with algebra.
apply Trans with (ring_mult x (monoid_unit R)); auto with algebra.
Qed.
End Lemmas.
Hint Resolve RING_assoc RING_comp RING_unit_r RING_unit_l RING_dist_r
RING_dist_l RING_absorbant_r RING_absorbant_l RING_op_mult_l
RING_op_mult_r: algebra.
Section Commutative_rings.
Variable R1 : CRING.

Lemma CRING_com : forall x y : R1, Equal (ring_mult x y) (ring_mult y x).
exact (cring_com_prf R1).