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)).

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