(** Note: the <= in the conclusion is likely tight *)

(* Specifications: *)
Lemma CRealLt_QR_to_single_dist : forall (q : Q) (x : CReal) (n : Z),
inject_Q q < x -> (-(2^n) <= seq x n - q)%Q.
Lemma CRealLt_RQ_to_single_dist : forall (x : CReal) (q : Q) (n : Z),
x < inject_Q q -> (-(2^n) <= q - seq x n)%Q.
Lemma Pos2Z_pos_is_pos : forall (p : positive),
(1 <= Z.pos p)%Z.
Lemma Qabs_Qgt_condition: forall x y : Q,
(x < Qabs y)%Q <-> (x < y \/ x < -y)%Q.
Lemma CReal_from_cauchy_seq_bound :
forall (xn : nat -> CReal) (xcau : Un_cauchy_mod xn) (i j : Z),
(Qabs (CReal_from_cauchy_seq xn xcau i - CReal_from_cauchy_seq xn xcau j) <= 1)%Q.