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

Lemma CRmorph_plus : forall {R1 R2 : ConstructiveReals}
(f : @ConstructiveRealsMorphism R1 R2)
(x y : CRcarrier R1),
CRmorph f (CRplus R1 x y)
== CRplus R2 (CRmorph f x) (CRmorph f y).