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.