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

Lemma CRmorph_mult_inv : forall {R1 R2 : ConstructiveReals} (f : @ConstructiveRealsMorphism R1 R2) (x : CRcarrier R1) (p : positive), CRmorph f (CRmult R1 x (CR_of_Q R1 (1 # p))) == CRmult R2 (CRmorph f x) (CR_of_Q R2 (1 # p)).