Section Monoid.
Variable M : ABELIAN_MONOID.
change
(forall x y : M:ABELIAN_SGROUP, Equal (sgroup_law _ x y) (sgroup_law _ y x))
in |- *; auto with algebra.
Qed.

Lemma ABELIAN_MONOID_permute :
forall x y z : M,
Equal (sgroup_law _ x (sgroup_law _ y z))
(sgroup_law _ y (sgroup_law _ x z)).