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_transitivity :
forall A B C D E F : Point, Cong A B E F -> Cong C D E F -> Cong A B C D.