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 th19: forall O A B O1 A1 B1 O2 A2 B2, ~ ColH O A B -> ~ ColH O1 A1 B1 -> ~ ColH O2 A2 B2 -> CongaH A O B A1 O1 B1 -> CongaH A O B A2 O2 B2 -> CongaH A1 O1 B1 A2 O2 B2.