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 colH_IncidL__IncidL : forall A B C l,
A<>B ->
IncidL A l ->
IncidL B l ->
ColH A B C ->
IncidL C l.