Definition IQR (q : Q) := Rabst (inject_Q q).

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}}.