Section Order.
Context `{T2D:Tarski_2D}.
Context `{TE:@Tarski_euclidean Tn TnEQD}.
(* sum_preserves leP : a <= x /\ b <= y => a + b <= x + y *)
(** Lemma 14.40 states that we have an ordered field. *)

Lemma compatibility_of_sum_with_order : forall O E E' A B C APC BPC,
LeP O E E' A B -> Sum O E E' A C APC -> Sum O E E' B C BPC ->
LeP O E E' APC BPC.