proposition: Lemma lemma_samenotopposite : forall A B C D, OS A B C D -> ~ TS A C D B.
proof: Proof. intros. assert (OS B A C D) by (forward_using lemma_samesidesymmetric). assert (~ TS A C D B). { intro. assert (TS B C D B) by (conclude lemma_planeseparation). let Tf:=fresh in assert (Tf:exists M, BetS B M B) by (conclude_def TS );destruct Tf as [M];spliter. assert (~ BetS B M B) by (conclude axiom_betweennessidentity). contradict. } close. Qed.
imports: GeoCoq.Elements.OriginalProofs.lemma_samesidesymmetric GeoCoq.Elements.OriginalProofs.lemma_planeseparation