Add Parametric Morphism : inject_Q
    with signature Qeq ==> CRealEq
      as inject_Q_morph.#[global]
Instance inject_Q_morph_T
  : CMorphisms.Proper
      (CMorphisms.respectful Qeq CRealEq) inject_Q.(** * Algebraic operations *)

(** We reduce the rational numbers to accelerate calculations. *)
Definition CReal_plus_seq (x y : CReal) :=
  (fun n : Z => Qred (seq x (n-1)%Z + seq y (n-1)%Z)).Definition CReal_plus_scale (x y : CReal) : Z :=
  Z.max x.(scale) y.(scale) + 1.

Lemma CReal_plus_cauchy : forall (x y : CReal), QCauchySeq (CReal_plus_seq x y).