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

Lemma CRmorph_appart : forall {R1 R2 : ConstructiveReals}
(f : @ConstructiveRealsMorphism R1 R2)
(x y : CRcarrier R1)
(app : x ≶ y),
CRmorph f x ≶ CRmorph f y.