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.

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.