Definition DRealRepr (x : DReal) : CReal :=
{|
seq := CReal_of_DReal_seq x;
scale := CReal_of_DReal_scale x;
cauchy := CReal_of_DReal_cauchy x;
bound := CReal_of_DReal_bound x
|}.
(** ** Order for DReal *)
Definition Rle (x y : DReal)
:= forall q:Q, proj1_sig x q = true -> proj1_sig y q = true.

Lemma DRealReprQ : forall (x : DReal) (q : Q),
proj1_sig x q = true
-> CRealLt (inject_Q q) (DRealRepr x).