Section Lemmas.
Variable E : MONOID.
intros; apply (monoid_unit_r_prf E x).
Qed.
intros; apply (monoid_unit_l_prf E x).
Qed.

Lemma MONOID_unit_unique :
forall e : E,
(forall x : E, Equal (sgroup_law _ x e) x) ->
(forall x : E, Equal (sgroup_law _ e x) x) -> Equal e (monoid_unit E).