proposition: Lemma Sumx_resp_leEq : forall n (f g : forall i, i < n -> R), (forall i H, f i H [<=] g i H) -> Sumx f [<=] Sumx g.
proof: Proof. simple induction n. intros; simpl in |- *; apply leEq_reflexive. clear n; intros; simpl in |- *. apply plus_resp_leEq_both. apply H; intros; apply H0. apply H0. Qed.
imports: CoRN.algebra.COrdFields Coq(Lia)