Section Archimedes_for_angles.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma angles_archi_aux :
forall A B C D E F G H I,
GradA A B C D E F -> GradA A B C G H I -> ~ SAMS D E F G H I ->
exists P Q R, GradA A B C P Q R /\ ~ SAMS P Q R A B C.