Section Archimedes_for_angles.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(** Inspired by Hartshorne's demonstration of Lemma 35.1 in Geometry Euclid and Beyond *)
Lemma archi_in_angles :
archimedes_axiom ->
forall A B C D E F,
~ Col A B C -> D <> E -> F <> E ->
exists P Q R, GradA A B C P Q R /\ (LeA D E F P Q R \/ ~ SAMS P Q R A B C).