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 lt_diff_ps : forall O E E' X Y XMY,
Col O E X -> Col O E Y -> LtP O E E' Y X -> Diff O E E' X Y XMY -> Ps O E XMY.