Section Euclid.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

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).