Definition CR_Q_limit {R : ConstructiveReals} (x : CRcarrier R) (n:nat)
: { q:Q  &  x < CR_of_Q R q < x + CR_of_Q R (1 # Pos.of_nat n) }.

Lemma CR_Q_limit_cv : forall {R : ConstructiveReals} (x : CRcarrier R),
CR_cv R (fun n => CR_of_Q R (let (q,_) := CR_Q_limit x n in q)) x.