proposition: Lemma sum4_col : forall O E E' A B C D S, Sum4 O E E' A B C D S -> ~Col O E E' /\ Col O E A /\ Col O E B /\ Col O E C /\ Col O E D /\ Col O E S.
proof: Proof. intros. unfold Sum4 in H. ex_and H ABC. assert(HH:=sum3_col O E E' A B C ABC H). assert(Ar2 O E E' ABC D S). apply sum_ar2; auto. unfold Ar2 in *. spliter. repeat split; auto. Qed.
imports: GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg