Qed.

(* Specifications: *)
Lemma S_1 : forall A B C : Point, S A B C = S B C A.
auto with Geom.
Theorem multnonzero: forall a b: F, a*b<>0 -> a<>0 /\ b<>0.
intros a b H1; split; intros H2; case H1; rewrite H2;ring.
Theorem multnonzero_l: forall a b: F, a*b<>0 -> a<>0.
intros a b H1; intros H2; case H1; rewrite H2;ring.
Theorem multnonzero_r: forall a b: F, a*b<>0 -> b<>0.
intros a b H1; intros H2; case H1; rewrite H2;ring.
Lemma inverse_ratio : forall a b, a<>0 -> b<>0 -> a/b = 1 / (b/a).
Hint Resolve field_prop_1 field_prop_3 field_prop_4 field_prop_5 opzero
nonzeromult nonzerodiv nonzeroinv inverse_ratio : field_hints.
Lemma Lcmult2 : forall a b c : F, a <> 0 -> a * b = c -> b = c / a.
intros.