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 same_side_prime_not_colH : forall A B C D,
same_side' A B C D -> ~ ColH A C D /\ ~ ColH B C D.