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)).