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 le_pos_prod_le : forall O E E' A B C AC BC,
LeP O E E' A B -> LeP O E E' O C ->
Prod O E E' A C AC -> Prod O E E' B C BC ->
LeP O E E' AC BC.