Section Hom_lemmas.
Hint Resolve RING_comp: algebra.
Variable R R' : RING.
Variable f : Hom R R'.
case f; auto with algebra.
Qed.
case f; auto with algebra.
Qed.

Lemma RING_hom_ext :
forall f g : Hom R R', (forall x : R, Equal (f x) (g x)) -> Equal f g.