intros x y z; try assumption.
unfold field_div in |- *.
auto with algebra.
Qed.
Hint Resolve FIELD_mult_div_l: algebra.

Lemma FIELD_div_div2 :
forall x y z : K,
~ Equal y (monoid_unit K) ->
~ Equal z (monoid_unit K) ->
Equal (field_div (field_div x y) z) (field_div x (ring_mult z y)).