proposition: Lemma CFIELD_inverse_law2 : forall x y : K, ~ Equal x (monoid_unit K) -> ~ Equal y (monoid_unit K) -> Equal (field_inverse (ring_mult x y)) (ring_mult (field_inverse x) (field_inverse y)).
proof: Proof. intros x y H' H'0; try assumption. apply Trans with (ring_mult (field_inverse y) (field_inverse x):K); auto with algebra. Qed.
imports: Field_facts Cfield_cat