#[global]
Instance seq_cv_morph
  : forall (un : nat -> CReal), CMorphisms.Proper
      (CMorphisms.respectful CRealEq CRelationClasses.iffT) (seq_cv un).(* Sharpen the archimedean property : constructive versions of
   the usual floor and ceiling functions. *)
Definition Rfloor (a : CReal)
  : { p : Z  &  inject_Q (p#1) < a < inject_Q (p#1) + 2 }.

Lemma CReal_cv_self : forall (x : CReal) (n : positive), CReal_abs (x - inject_Q (seq x (Z.neg n))) <= inject_Q (1#n).