Section Lemmas.
Variable R : RING.
exact (sgroup_assoc_prf (E:=R) (ring_monoid R)).
Qed.
unfold ring_mult in |- *; auto with algebra.
Qed.
exact (monoid_unit_r_prf (ring_monoid R)).
Qed.
exact (monoid_unit_l_prf (ring_monoid R)).
Qed.
exact (ring_dist_r_prf R).
Qed.
exact (ring_dist_l_prf R).
Qed.
Hint Resolve RING_assoc RING_comp RING_unit_r RING_unit_l RING_dist_r
RING_dist_l: algebra.

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