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 th15: forall H K O L H' K' O' L',
~ ColH H O L -> ~ ColH H' O' L' -> ~ ColH K O L -> ~ ColH K' O' L' ->
~ ColH H O K -> ~ ColH H' O' K' ->
(cut' H K O L /\ cut' H' K' O' L') \/ (same_side' H K O L /\ same_side' H' K' O' L') ->
CongaH H O L H' O' L' -> CongaH K O L K' O' L' ->
CongaH H O K H' O' K'.