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 line_col : forall A B C l, IncidL A l -> IncidL B l -> IncidL C l -> Col A B C.