Section Lemmas1.
Variable K : CFIELD.
exact (cring_com_prf K).
Qed.
Hint Immediate CFIELD_com: algebra.
intros x y H' H'0; try assumption.
apply Trans with (ring_mult (field_inverse y) (field_inverse x):K);
auto with algebra.
Qed.
Hint Resolve CFIELD_inverse_law2: algebra.

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