proposition: Lemma Diff_Col_ColB : forall A B C, Col A B C -> ColB A B C.
proof: Proof. intros A B C H. unfold Col in H. unfold ColB. intro HColB. destruct HColB as [HNT1 [HNT2 HNT3]]. apply NT_NBet in HNT1. apply NT_NBet in HNT2. apply NT_NBet in HNT3. elim H. intro HBet; contradiction. intro HColAux; elim HColAux; intro HBet; clear HColAux. apply between_symmetry in HBet. contradiction. contradiction. Qed.
imports: GeoCoq.Axioms.beeson_s_axioms GeoCoq.Tarski_dev.Ch08_orthogonality