unfold not in |- *.
intros x y H' H'0; try assumption.
absurd (Equal (ring_mult x y) (monoid_unit K)); auto with algebra.
apply Trans with (ring_mult (monoid_unit K) y:K); auto with algebra.
Qed.

Lemma FIELD_integral_domain_r :
forall x y : K,
~ Equal (ring_mult x y) (monoid_unit K) -> ~ Equal y (monoid_unit K).