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.".
exact (CRING_mult4 (R1:=K)).
Qed.
Hint Resolve CRING_mult4: algebra.
exact (CRING_mult3 (R1:=K)).
Qed.
Hint Resolve CFIELD_mult3: algebra.
exact (CRING_mult3bis (R1:=K)).
Qed.
Hint Resolve CFIELD_mult3bis: algebra.

Lemma CFIELD_mult_div_r :
forall x y z : K,
Equal (ring_mult (field_div y z) x) (field_div (ring_mult y x) z).