Definition same_side' := fun A B X Y =>
  X <> Y /\ forall l, IncidentL X l -> IncidentL Y l -> same_side A B l.

Lemma axiom_hcong_4_uniqueness : forall A B C O P X Y Y', ~ Col_H P O X -> ~ Col_H A B C -> CongA A B C X O Y -> CongA A B C X O Y' -> same_side' P Y O X -> same_side' P Y' O X -> outH O Y Y'.