proposition: Lemma lemma_NCorder : forall A B C, nCol A B C -> nCol B A C /\ nCol B C A /\ nCol C A B /\ nCol A C B /\ nCol C B A.
proof: Proof. intros. assert (~ Col B A C). { intro. assert (Col A B C) by (forward_using lemma_collinearorder). contradict. } assert (~ Col B C A). { intro. assert (Col A B C) by (forward_using lemma_collinearorder). contradict. } assert (~ Col C A B). { intro. assert (Col A B C) by (forward_using lemma_collinearorder). contradict. } assert (~ Col A C B). { intro. assert (Col A B C) by (forward_using lemma_collinearorder). contradict. } assert (~ Col C B A). { intro. assert (Col A B C) by (forward_using lemma_collinearorder). contradict. } close. Qed.
imports: GeoCoq.Elements.OriginalProofs.lemma_collinearorder