Definition CRmorph_compose {R1 R2 R3 : ConstructiveReals}
           (f : @ConstructiveRealsMorphism R1 R2)
           (g : @ConstructiveRealsMorphism R2 R3)
  : @ConstructiveRealsMorphism R1 R3.

Lemma CRmorph_rat_cv : forall {R1 R2 : ConstructiveReals} (qn : nat -> Q), CR_cauchy R1 (fun n => CR_of_Q R1 (qn n)) -> CR_cauchy R2 (fun n => CR_of_Q R2 (qn n)).