Definition field_inverse (x : K) : K := Ap (field_inverse_map K) x.Definition field_div (x y : K) : K := ring_mult x (field_inverse y).

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