proposition: Lemma mult_resp_leEq_both : forall x x' y y' : R, [0] [<=] x -> [0] [<=] y -> x [<=] x' -> y [<=] y' -> x[*]y [<=] x'[*]y'.
proof: Proof. intros. apply leEq_transitive with (x[*]y'). apply mult_resp_leEq_lft; assumption. apply mult_resp_leEq_rht. assumption. apply leEq_transitive with y; assumption. Qed.
imports: CoRN.algebra.COrdFields Coq(Lia)