Definition same_side := fun A B l => exists P, cut l A P /\ cut l B P.

(* Specifications: *)
Lemma same_side_one_side : forall A B l, same_side A B l -> OS (P1 l) (P2 l) A B.
Lemma one_side_same_side : forall A B l, OS (P1 l) (P2 l) A B -> same_side A B l.