intros x y z; try assumption.
apply Trans with (ring_mult z (ring_mult x y)); auto with algebra.
apply Trans with (ring_mult z (ring_mult y x)); auto with algebra.
apply Trans with (ring_mult y (ring_mult z x)); auto with algebra.
apply Trans with (ring_mult (ring_mult z x) y); auto with algebra.
Qed.
Hint Resolve CRING_mult3bis: algebra.
End Commutative_rings.
Hint Resolve CRING_mult4 CRING_mult3 CRING_mult3bis: algebra.
Hint Immediate CRING_com: algebra.
Section Hom_lemmas.
Hint Resolve RING_comp: algebra.
Variable R R' : RING.
Variable f : Hom R R'.

Lemma RING_hom_prop :
forall x y : R, Equal (f (ring_mult x y)) (ring_mult (f x) (f y)).