Section Lemmas1.
Variable K : CFIELD.
exact (cring_com_prf K).
Qed.
Hint Immediate CFIELD_com: algebra.

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)).