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.