Theorem equivalent_postulates_with_decidability_of_intersection_of_lines : decidability_of_intersection -> all_equiv (alternate_interior_angles_postulate:: alternative_playfair_s_postulate:: alternative_proclus_postulate:: alternative_strong_parallel_postulate:: consecutive_interior_angles_postulate:: euclid_5:: euclid_s_parallel_postulate:: inverse_projection_postulate:: midpoint_converse_postulate:: perpendicular_transversal_postulate:: playfair_s_postulate:: universal_posidonius_postulate:: postulate_of_parallelism_of_perpendicular_transversals:: postulate_of_transitivity_of_parallelism:: proclus_postulate:: strong_parallel_postulate:: tarski_s_parallel_postulate:: triangle_circumscription_principle:: nil).