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 five_segment :
forall A A' B B' C C' D D' : Point,
Cong A B A' B' ->
Cong B C B' C' ->
Cong A D A' D' ->
Cong B D B' D' -> Bet A B C -> Bet A' B' C' -> A <> B -> Cong C D C' D'.