proposition: Lemma col_alt_def : forall A B C, Col Point Bet A B C <-> (A = P1 /\ B = P1 /\ C = P1) \/ (A <> P1 /\ B <> P1) \/ (B <> P1 /\ C <> P1) \/ (A <> P1 /\ C <> P1).
proof: Proof. unfold Col. split. destruct A, B, C ; unfold Bet ; try tauto; intros; right; try (left ; split ; discriminate); right; try (left ; split ; discriminate); right; split ; discriminate. destruct A, B, C; simpl; try tauto; intro ; intuition; spliter ; discriminate. Qed.
imports: GeoCoq.Meta_theory.Counter_models.Planar.independence