proposition: Theorem legendre_s_fourth_theorem : archimedes_axiom -> legendre_s_parallel_postulate -> postulate_of_existence_of_a_triangle_whose_angles_sum_to_two_rights.
proof: Proof. intros; apply triangle__existential_triangle, rah__triangle, legendre_s_fourth_theorem_aux; assumption. Qed.
imports: GeoCoq.Axioms.continuity_axioms GeoCoq.Axioms.parallel_postulates GeoCoq.Meta_theory.Parallel_postulates.SPP_ID GeoCoq.Meta_theory.Parallel_postulates.TCP_tarski GeoCoq.Meta_theory.Parallel_postulates.alternate_interior_angles_proclus GeoCoq.Meta_theory.Continuity.angle_archimedes GeoCoq.Meta_theory.Continuity.archimedes GeoCoq.Meta_theory.Continuity.aristotle GeoCoq.Meta_theory.Parallel_postulates.euclid_5_original_euclid GeoCoq.Meta_theory.Parallel_postulates.existential_triangle_rah GeoCoq.Meta_theory.Parallel_postulates.par_perp_perp_TCP GeoCoq.Meta_theory.Parallel_postulates.playfair_alternate_interior_angles GeoCoq.Meta_theory.Parallel_postulates.playfair_bis_playfair GeoCoq.Meta_theory.Parallel_postulates.playfair_universal_posidonius_postulate GeoCoq.Meta_theory.Parallel_postulates.proclus_SPP GeoCoq.Meta_theory.Parallel_postulates.rah_triangle GeoCoq.Meta_theory.Parallel_postulates.tarski_euclid GeoCoq.Meta_theory.Parallel_postulates.triangle_playfair_bis GeoCoq.Meta_theory.Parallel_postulates.triangle_existential_triangle GeoCoq.Meta_theory.Parallel_postulates.universal_posidonius_postulate_par_perp_perp GeoCoq.Tarski_dev.Annexes.defect