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.
intros x y H'; try assumption.
apply Trans with (ring_mult (field_div x y) y:K); auto with algebra.
Qed.
Hint Resolve CFIELD_simpl_l: algebra.
Comments "Normalisation.".

Lemma CFIELD_mult4 :
forall a b c d : K,
Equal (ring_mult (ring_mult a b) (ring_mult c d))
(ring_mult (ring_mult a c) (ring_mult b d)).