Section Archimedes_for_angles.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(** If Archimedes' postulate holds, every nondegenerate angle can be doubled until exceeding 90° *)
Lemma archi__gradaexp_destruction :
archimedes_axiom ->
forall A B C,
~ Col A B C ->
exists P Q R, GradAExp A B C P Q R /\ Obtuse P Q R.