unfold field_div in |- *.
intros x y z H' H'0; try assumption.
apply
Trans
with
(ring_mult x
(ring_mult (field_inverse (field_inverse z)) (field_inverse y))
:K); auto with algebra.
apply Trans with (ring_mult x (ring_mult z (field_inverse y)):K);
auto with algebra.
Qed.
Hint Resolve FIELD_div_div: algebra.
Comments "Normalisation.".

Lemma FIELD_mult_div_l :
forall x y z : K,
Equal (ring_mult x (field_div y z)) (field_div (ring_mult x y) z).