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 cong_preserves_bet : forall A B C A' B' C', A'<>B' -> B'<>C' -> A'<>C' ->
BetH A B C -> CongH A B A' B' -> CongH B C B' C' -> CongH A C A' C' ->
BetH A' B' C'.