Section Lemmas.
Variable E : MONOID.
intros; apply (monoid_unit_r_prf E x).
Qed.
intros; apply (monoid_unit_l_prf E x).
Qed.
intros e H' H'0; try assumption.
apply Trans with (sgroup_law _ e (monoid_unit E)); auto with algebra.
apply Sym.
apply MONOID_unit_r.
Qed.
Variable F : MONOID.
Variable f : Hom E F.

Lemma MONOID_hom_prop : Equal (f (monoid_unit E)) (monoid_unit F).