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 th18_aux:
forall A B C A' B' C',
~ ColH A B C ->
~ ColH A' B' C' ->
CongH A B A' B' ->
CongH A C A' C' ->
CongH B C B' C' ->
CongaH B A C B' A' C'.