Section Lemmas.
Variable R : INTEGRAL_DOMAIN.
exact (idomain_prf R).
Qed.
intros x y H'; try assumption.
generalize (INTEGRAL_DOMAIN_prop_rev (x:=x) (y:=y)).
apply NNPP; tauto.
Qed.

Lemma INTEGRAL_DOMAIN_mult_l :
forall x y : R,
~ Equal (ring_mult x y) (monoid_unit R) -> ~ Equal x (monoid_unit R).