Definition RInt (f : R -> V) (a b : R) := iota (is_RInt f a b).

Lemma is_RInt_le (f g : R -> R) (a b If Ig : R) : a <= b -> is_RInt f a b If -> is_RInt g a b Ig -> (forall x, a < x < b -> f x <= g x) -> If <= Ig.