proposition: Lemma inner_pasch' : forall A B C P Q, Bet A P C -> Bet B Q C -> A <> P -> P <> C -> B <> Q -> Q <> C -> ~ (Bet A B C \/ Bet B C A \/ Bet C A B) -> exists x : Tpoint, Bet P x B /\ Bet Q x A.
proof: Proof. intros A B C P Q; intros; apply inner_pasch with C; assumption. Qed.
imports: GeoCoq.Axioms.tarski_axioms GeoCoq.Axioms.gupta_inspired_variant_axioms GeoCoq.Tarski_dev.Ch05_bet_le