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 same_side_trans : forall A B C l,
same_side A B l -> same_side B C l -> same_side A C l.