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

Lemma CRplus_neg_rat_lt : forall {R : ConstructiveReals} (x : CRcarrier R) (q : Q), Qlt q 0 -> CRlt R (CRplus R x (CR_of_Q R q)) x.