End Euclid.
Section Euclidean.
Context `{TE:Tarski_euclidean}.

(* Specifications: *)
Lemma inter_dec : forall A B C D,
(exists I, Col I A B /\ Col I C D) \/ ~ (exists I, Col I A B /\ Col I C D).
Lemma aristotle : forall P Q A B C, ~ Col A B C -> Acute A B C ->
exists X Y, Out B A X /\ Out B C Y /\ Per B X Y /\ Lt P Q X Y.
Lemma greenberg : forall P Q R A B C, ~ Col A B C ->
Acute A B C -> Q <> R -> Per P Q R ->
exists S, LtA P S Q A B C /\ Out Q S R.
Theorem postulates_in_euclidean_context : forall P, List.In P
(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) ->
P.