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_prod_with_order : forall O E E' A B AB,
LeP O E E' O A -> LeP O E E' O B -> Prod O E E' A B AB ->
LeP O E E' O AB.