proposition: Lemma sign_dec : forall O E A, Col O E A -> O <> E -> A = O \/ Ps O E A \/ Ng O E A.
proof: Proof. intros. induction(eq_dec_points A O). left; auto. assert(HH:= third_point O E A H). induction HH. { right;right. unfold Ng. repeat split; auto. } { right;left. unfold Ps. unfold Out. repeat split; auto. } Qed.
imports: GeoCoq.Tarski_dev.Ch14_order