Definition ZCG_prove (f : ZCGForm) :=
  CG_prove Z 0%Z Zplus Zopp Zle_bool 1%Z (ZCGtranslate f).

(* Specifications: *)
Theorem ZCG_prove_correct : forall f : ZCGForm, ZCG_prove f = true -> forall rho : ad -> Z, rho N0 = 0%Z -> ZCGeval rho f.
Theorem ZCG_prove_complete : forall f : ZCGForm, (forall rho : ad -> Z, rho N0 = 0%Z -> ZCGeval rho f) -> ZCG_prove f = true.