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 congaH_commr : forall A B C D E F, ~ColH A B C -> ~ColH D E F -> CongaH A B C D E F -> CongaH A B C F E D.