proposition: Lemma diff_exists : forall O E E' A B, ~Col O E E' -> Col O E A -> Col O E B -> exists D, Diff O E E' A B D.
proof: Proof. intros. assert(Hop:=opp_exists O E E' H B H1). ex_and Hop MB. assert(Col O E MB). unfold Opp in H2. unfold Sum in H2. spliter. unfold Ar2 in H2. tauto. assert(HS:=sum_exists O E E' H A MB H0 H3). ex_and HS C. exists C. unfold Diff. exists MB. split; assumption. Qed.
imports: GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg