Definition DRealAbstr : CReal -> DReal.
Definition DRealQlimExp2 (x : DReal) (n : nat)
: { q : Q | proj1_sig x q = true /\ proj1_sig x (q + (1#(Pos.of_nat (2^n)%nat)))%Q = false }.
Definition CReal_of_DReal_seq (x : DReal) (n : Z) :=
proj1_sig (DRealQlimExp2 x (Z.to_nat (-n))).

(* Specifications: *)
Lemma CReal_of_DReal_cauchy (x : DReal) :
QCauchySeq (CReal_of_DReal_seq x).
Lemma CReal_of_DReal_seq_max_prec_1 : forall (x : DReal) (n : Z),
(n>=0)%Z -> CReal_of_DReal_seq x n = CReal_of_DReal_seq x 0.
Lemma CReal_of_DReal_seq_bound :
forall (x : DReal) (i j : Z),
(Qabs (CReal_of_DReal_seq x i - CReal_of_DReal_seq x j) <= 1)%Q.