proposition: Lemma osp_dec : forall A B C X Y, OSP A B C X Y \/ ~ OSP A B C X Y.
proof: Proof. intros A B C X Y. destruct (cop_dec A B C X) as [|HX]. right; intros [X' [[Ha _] _]]; apply Ha; assumption. destruct (tsp_exists A B C X HX) as [X']. destruct (tsp_dec A B C Y X') as [|HNTS]. left; exists X'; split; assumption. right; intro; apply HNTS; apply l9_41_2 with X; assumption. Qed.
imports: GeoCoq.Tarski_dev.Ch10_line_reflexivity_2