(* The constructive equality on R. *)
Definition Req_constr (x y : R) : Prop
:= (x < y -> False) /\ (y < x -> False).

Lemma Rcomplete : forall xn : nat -> R,
(forall p : positive,
{n : nat |
forall i j : nat,
(n <= i)%nat -> (n <= j)%nat -> IQR (1 # p) < Rabst (CReal_abs (Rrepr (xn i + - xn j))) -> False}) ->
{l : R &
forall p : positive,
{n : nat |
forall i : nat, (n <= i)%nat -> IQR (1 # p) < Rabst (CReal_abs (Rrepr (xn i + - l))) -> False}}.