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.Global Instance same_side_morphism : Proper(eq ==> eq ==> EqL ==> iff) same_side.

Lemma IncidL_not_IncidL__not_colH :forall A B C l, A<>B -> IncidL A l -> IncidL B l -> ~ IncidL C l -> ~ ColH A B C.