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

Lemma CRmorph_inv : forall {R1 R2 : ConstructiveReals} (f : @ConstructiveRealsMorphism R1 R2) (x : CRcarrier R1) (xnz : x ≶ 0) (fxnz : CRmorph f x ≶ 0), CRmorph f ((/ x) xnz) == (/ CRmorph f x) fxnz.