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 out_same_side' : forall X Y A B C l , X <> Y ->
IncidL X l -> IncidL Y l -> IncidL A l -> ~ IncidL B l-> outH A B C ->
same_side' B C X Y.