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

Lemma CRmorph_plus_rat : forall {R1 R2 : ConstructiveReals}
(f : @ConstructiveRealsMorphism R1 R2)
(x : CRcarrier R1) (q : Q),
CRmorph f (CRplus R1 x (CR_of_Q R1 q))
== CRplus R2 (CRmorph f x) (CR_of_Q R2 q).