(** Same side predicate corresponds to OS of Tarski. *)

Lemma one_side_same_side : forall A B l, OS (P1 l) (P2 l) A B -> same_side A B l.
Definition same_side' := fun A B X Y =>
X <> Y /\ forall l, IncidentL X l -> IncidentL Y l -> same_side A B l.