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_P11 :
forall (f:R -> R) (a b l:R) (un:nat -> posreal)
(phi1 phi2 psi1 psi2:nat -> StepFun a b),
Un_cv un 0 ->
(forall n:nat,
(forall t:R,
Rmin a b <= t <= Rmax a b -> Rabs (f t - phi1 n t) <= psi1 n t) /\
Rabs (RiemannInt_SF (psi1 n)) < un n) ->
(forall n:nat,
(forall t:R,
Rmin a b <= t <= Rmax a b -> Rabs (f t - phi2 n t) <= psi2 n t) /\
Rabs (RiemannInt_SF (psi2 n)) < un n) ->
Un_cv (fun N:nat => RiemannInt_SF (phi1 N)) l ->
Un_cv (fun N:nat => RiemannInt_SF (phi2 N)) l.