(** This development is inspired by The Foundations of Geometry and the Non-Euclidean Plane, by George E Martin, chapter 22 *)
Section Archimedes.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(** For every m, there exists n such that A0Dm = A0An - E0En = n(A0A1 - E0E1) (m=n) *)
Lemma t22_18_aux1 : forall A0 A1 E0 E1 D1 D,
Bet A0 D1 A1 -> Cong E0 E1 A1 D1 ->
Grad A0 D1 D ->
exists A E, Grad2 A0 A1 A E0 E1 E /\ Cong E0 E A D /\ Bet A0 D A.