proposition: Theorem szmielew_s_theorem : aristotle_s_axiom -> (forall P : Prop, (playfair_s_postulate -> P) -> (hyperbolic_plane_postulate -> ~ P)-> (P <-> playfair_s_postulate)).
proof: Proof. intro H; intros. assert (L := aah__hpp). assert (HE := aristotle__acute_or_right H). assert (HG := aristotle__greenberg H). elim (equivalent_postulates_assuming_greenberg_s_axiom HG playfair_s_postulate postulate_of_right_saccheri_quadrilaterals); unfold List.In; tauto. Qed.
imports: GeoCoq.Axioms.continuity_axioms GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates