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 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'.