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Definition RiemannInt (f:R -> R) (a b:R) (pr:Riemann_integrable f a b) : R :=
  let (a,_) := RiemannInt_exists pr RinvN RinvN_cv in a.

(* Specifications: *)
Lemma RiemannInt_P5 : forall (f:R -> R) (a b:R) (pr1 pr2:Riemann_integrable f a b), RiemannInt pr1 = RiemannInt pr2.
Lemma maxN : forall (a b:R) (del:posreal), a < b -> { n:nat | a + INR n * del < b /\ b <= a + INR (S n) * del }.