proposition: Lemma per_not_col : forall A B C, A <> B -> B <> C -> Per A B C -> ~Col A B C.
proof: Proof. intros. intro. unfold Per in H1. ex_and H1 C'. assert (C = C' \/ Midpoint A C C'). apply l7_20. ColR. assumption. induction H4;treat_equalities; intuition. Qed.
imports: GeoCoq.Tarski_dev.Ch07_midpoint GeoCoq.Tactics.Coinc.ColR