Fixpoint SubEquiN (N:nat) (x y:R) (del:posreal) : list R :=
  match N with
    | O => cons y nil
    | S p => cons x (SubEquiN p (x + del) y del)
  end.Definition max_N (a b:R) (del:posreal) (h:a < b) : nat :=
  let (N,_) := maxN del h in N.Definition SubEqui (a b:R) (del:posreal) (h:a < b) : list R :=
  SubEquiN (S (max_N del h)) a b del.

Lemma RiemannInt_P19 : forall (f g:R -> R) (a b:R) (pr1:Riemann_integrable f a b) (pr2:Riemann_integrable g a b), a <= b -> (forall x:R, a < x < b -> f x <= g x) -> RiemannInt pr1 <= RiemannInt pr2.