Require Export GeoCoq.Tarski_dev.Ch14_prod.
Section Order.
Context `{T2D:Tarski_2D}.
Context `{TE:@Tarski_euclidean Tn TnEQD}.

(* sum_preserves leP : a <= x /\ b <= y => a + b <= x + y *)
Lemma leP_sum_leP : forall O E E' A B C X Y Z,
LeP O E E' A X -> LeP O E E' B Y -> Sum O E E' A B C -> Sum O E E' X Y Z ->
LeP O E E' C Z.