change
(forall x y z t : M:ABELIAN_SGROUP,
Equal (sgroup_law _ (sgroup_law _ x y) (sgroup_law _ z t))
(sgroup_law _ (sgroup_law _ x z) (sgroup_law _ y t)))
in |- *; auto with algebra.
Qed.
End Monoid.
Hint Immediate ABELIAN_MONOID_com ABELIAN_MONOID_permute ABELIAN_MONOID4:
algebra.
Section Group.
Variable G : ABELIAN_GROUP.

Lemma ABELIAN_GROUP_com :
forall x y : G, Equal (sgroup_law _ x y) (sgroup_law _ y x).