proposition: Lemma lemma_samesideflip : forall A B P Q, OS P Q A B -> OS P Q B A.
proof: Proof. intros. let Tf:=fresh in assert (Tf:exists p q r, (Col A B p /\ Col A B q /\ BetS P p r /\ BetS Q q r /\ nCol A B P /\ nCol A B Q)) by (conclude_def OS );destruct Tf as [p[q[r]]];spliter. assert (Col B A p) by (forward_using lemma_collinearorder). assert (Col B A q) by (forward_using lemma_collinearorder). assert (nCol B A P) by (forward_using lemma_NCorder). assert (nCol B A Q) by (forward_using lemma_NCorder). assert (OS P Q B A) by (conclude_def OS ). close. Qed.
imports: GeoCoq.Elements.OriginalProofs.lemma_NCorder