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).