intros x H'; try assumption.
apply FIELD_reg_right with (field_inverse x); auto with algebra.
apply Trans with (ring_unit K:K); auto with algebra.
apply Sym; auto with algebra.
Qed.
Hint Resolve FIELD_inverse_inverse: algebra.

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