Theorem equivalence_of_aristotle_greenberg_and_decidability_of_intersection : all_equiv_under (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) (aristotle_s_axiom:: greenberg_s_axiom:: decidability_of_intersection:: nil).