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 betH_congH2__False : forall A B C A' B' C', BetH A B C -> BetH A' C' B' -> CongH A B A' B' -> CongH A C A' C' -> False.