(** This is a weakened form of CRealLt_aboveSig which a special shape of eps needed below *)

(* The CRealLt index separates the Cauchy sequences *)
Lemma CRealLt_above_same : forall (x y : CReal) (n : Z),
(2 * 2 ^ n < seq y n - seq x n)%Q
-> forall p:Z, (p <= n)%Z -> Qlt (seq x p) (seq y p).