Section Lemmas.
Variable E : SGROUP.
intros x y z; try assumption.
apply (sgroup_assoc_prf E x y z); auto with algebra.
Qed.

Lemma SGROUP_comp :
forall x x' y y' : E,
Equal x x' -> Equal y y' -> Equal (sgroup_law _ x y) (sgroup_law _ x' y').