Theorem equivalent_postulates_assuming_archimedes_axiom : archimedes_axiom -> all_equiv (alternate_interior_angles_postulate:: alternative_playfair_s_postulate:: alternative_proclus_postulate:: alternative_strong_parallel_postulate:: bachmann_s_lotschnittaxiom:: consecutive_interior_angles_postulate:: euclid_5:: euclid_s_parallel_postulate:: existential_playfair_s_postulate:: existential_thales_postulate:: inverse_projection_postulate:: legendre_s_parallel_postulate:: midpoint_converse_postulate:: perpendicular_transversal_postulate:: postulate_of_transitivity_of_parallelism:: playfair_s_postulate:: posidonius_postulate:: universal_posidonius_postulate:: postulate_of_existence_of_a_right_lambert_quadrilateral:: postulate_of_existence_of_a_right_saccheri_quadrilateral:: postulate_of_existence_of_a_triangle_whose_angles_sum_to_two_rights:: postulate_of_existence_of_similar_triangles:: postulate_of_parallelism_of_perpendicular_transversals:: postulate_of_right_lambert_quadrilaterals:: postulate_of_right_saccheri_quadrilaterals:: postulate_of_transitivity_of_parallelism:: proclus_postulate:: strong_parallel_postulate:: tarski_s_parallel_postulate:: thales_postulate:: thales_converse_postulate:: triangle_circumscription_principle:: triangle_postulate:: weak_inverse_projection_postulate:: weak_tarski_s_parallel_postulate:: weak_triangle_circumscription_principle:: nil).