proposition: Lemma sum3_col : forall O E E' A B C S, sum3 O E E' A B C S -> ~Col O E E' /\ Col O E A /\ Col O E B /\ Col O E C /\ Col O E S.
proof: Proof. intros. unfold sum3 in H. ex_and H AB. assert(Ar2 O E E' A B AB). apply sum_ar2; auto. assert(Ar2 O E E' AB C S). apply sum_ar2; auto. unfold Ar2 in *. spliter. repeat split; auto. Qed.
imports: GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg