(** If the elements x(n) and y(n) of two Cauchy sequences x and are apart by at least 2*eps(n), we can find a k such that all further elements of the sequences are apart by at least 2*eps(k) *)

(* Specifications: *)
Lemma CRealLt_aboveSig : forall (x y : CReal) (n : Z),
(2 * 2^n < seq y n - seq x n)%Q
-> let (k, _) := QarchimedeanExp2_Z (/(seq y n - seq x n - (2 * 2 ^ n)%Q))
in forall p:Z,
(p <= n)%Z
-> (2^(-k) < seq y p - seq x p)%Q.