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 x (monoid_unit K):K); auto with algebra.
Qed.

Lemma FIELD_law_inverse :
forall x y : K,
Equal (ring_mult x y) (ring_unit K) -> Equal (field_inverse x) y.