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 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.