Section Euclid.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

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).