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