(* We use <= in sort Prop rather than < in sort Set,
   it is equivalent for the definition of limits and it
   extracts smaller programs. *)
Definition seq_cv (un : nat -> CReal) (l : CReal) : Set
  := forall p : positive,
    { n : nat  |  forall i:nat, le n i -> CReal_abs (un i - l) <= inject_Q (1#p) }.Definition Un_cauchy_mod (un : nat -> CReal) : Set
  := forall p : positive,
    { n : nat  |  forall i j:nat, le n i -> le n j
                       -> CReal_abs (un i - un j) <= inject_Q (1#p) }.

Lemma seq_cv_proper : forall (un : nat -> CReal) (a b : CReal), seq_cv un a -> a == b -> seq_cv un b.