Theorem equivalent_postulates_without_decidability_of_intersection_of_lines : all_equiv (alternate_interior_angles_postulate:: alternative_playfair_s_postulate:: consecutive_interior_angles_postulate:: midpoint_converse_postulate:: perpendicular_transversal_postulate:: playfair_s_postulate:: universal_posidonius_postulate:: postulate_of_parallelism_of_perpendicular_transversals:: postulate_of_transitivity_of_parallelism:: nil).