proposition: Lemma sum_Rle : forall {R : ConstructiveReals} (un vn : nat -> CRcarrier R) (n : nat), (forall k, le k n -> un k <= vn k) -> CRsum un n <= CRsum vn n.
proof: Proof. induction n. - intros. apply H. apply Nat.le_refl. - intros. simpl. apply CRplus_le_compat. + apply IHn. intros. apply H. apply (Nat.le_trans _ n _ H0). apply le_S, Nat.le_refl. + apply H. apply Nat.le_refl. Qed.
imports: QArith Qabs ConstructiveReals ConstructiveRealsMorphisms ConstructiveAbs ConstructiveLimits