intros x y a; try assumption.
unfold algebra_mult in |- *.
auto with algebra.
Qed.
Parameter
ALGEBRA_mult_lin_left :
forall (x y : A) (a : R),
Equal (algebra_mult (module_mult a x) y)
(module_mult a (algebra_mult x y)).
End Lemmas.
Hint Resolve ALGEBRA_comp ALGEBRA_lin_right ALGEBRA_lin_left
ALGEBRA_mult_lin_right ALGEBRA_mult_lin_left: algebra.
Section Lemmas2.
Variable R : CRING.
Variable A : ring_algebra R.

Lemma RING_ALGEBRA_assoc :
forall x y z : A,
Equal (algebra_mult (algebra_mult x y) z)
(algebra_mult x (algebra_mult y z)).