proposition: Lemma not_bet_diff : forall A B C, ~ (Bet A B C \/ Bet B C A \/ Bet C A B) -> A <> B /\ B <> C /\ A <> C.
proof: Proof. unfold Bet; intros. destruct A; destruct B; destruct C; intuition. Qed.
imports: GeoCoq.Axioms.tarski_axioms