Definition cut' A B X Y := X <> Y /\ forall l, IncidL X l -> IncidL Y l -> cut l A B.Global Instance cut_morphism : Proper(EqL ==> eq ==> eq ==> iff) cut.Global Instance same_side_morphism : Proper(eq ==> eq ==> EqL ==> iff) same_side.

Lemma pasch_general_case: forall A B C P Q : Point, 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 : Point, Bet P x B /\ Bet Q x A.