proposition: Lemma outside : forall A B C J P, CI J C A B /\ OutCirc P J <-> exists X, CI J C A B /\ Definitions.BetS C X P /\ tarski_axioms.Cong C X A B.
proof: Proof. intros. unfold OutCirc, CI. destruct J;destruct p. split. intros;spliter. decompose [ex and] H0;clear H0. exists x. inversion H; subst; auto. intros. decompose [ex and] H;clear H. inversion H0; subst;split; auto. exists x;auto. Qed.
imports: GeoCoq.Tarski_dev.Ch12_parallel GeoCoq.Axioms.euclidean_axioms GeoCoq.Axioms.continuity_axioms GeoCoq.Meta_theory.Continuity.elementary_continuity_props GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates