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))).

Lemma CReal_of_DReal_cauchy (x : DReal) :
QCauchySeq (CReal_of_DReal_seq x).