Section Lemmas.
Variable E : SGROUP.
intros x y z; try assumption.
apply (sgroup_assoc_prf E x y z); auto with algebra.
Qed.
unfold sgroup_law in |- *; auto with algebra.
Qed.
Variable F : SGROUP.
Variable f : Hom E F.

Lemma SGROUP_hom_prop :
forall x y : E, Equal (f (sgroup_law _ x y)) (sgroup_law _ (f x) (f y)).