proposition: Lemma col_alt_def : forall A B C, Col Point Bet A B C <-> A = B \/ B = C \/ A = C.
proof: Proof. split. unfold Col. intros [? | [? | ?]]; destruct H as [? | [? | ?]]; subst ; tauto. unfold Col, Bet. tauto. Qed.
imports: GeoCoq.Meta_theory.Counter_models.Planar.independence