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 betH_congH2__False : forall A B C A' B' C',
BetH A B C ->
BetH A' C' B' ->
CongH A B A' B' ->
CongH A C A' C' -> False.