intros x y z; try assumption.
apply Trans with (ring_mult (ring_mult x y) z); auto with algebra.
apply Trans with (ring_mult (ring_mult y x) z); auto with algebra.
Qed.
Hint Resolve CRING_mult3: algebra.

Lemma CRING_mult3bis :
forall x y z : R1,
Equal (ring_mult (ring_mult x y) z) (ring_mult (ring_mult x z) y).