Parameter
  ALGEBRA_lin_left :
    forall x y z : A,
    Equal (algebra_mult (sgroup_law A x y) z)
      (sgroup_law A (algebra_mult x z) (algebra_mult y z)).

Lemma ALGEBRA_mult_lin_right : forall (x y : A) (a : R), Equal (algebra_mult x (module_mult a y)) (module_mult a (algebra_mult x y)).