proposition: Lemma INTEGRAL_DOMAIN_mult_n0_r : forall x y : R, Equal (ring_mult x y) (monoid_unit R) -> ~ Equal y (monoid_unit R) -> Equal x (monoid_unit R).
proof: Proof. intros x y H' H'0; try assumption. intuition. elim (INTEGRAL_DOMAIN_prop (x:=x) (y:=y)); auto with algebra. intros H'1; try assumption. absurd (Equal y (monoid_unit R)); auto with algebra. Qed.
imports: Integral_domain_cat Ring_facts Classical_Prop