Definition ZTautoChecker  (f : BFormula (Formula Z) Tauto.isProp) (w: list ZArithProof): bool :=
@tauto_checker (Formula Z) (NFormula Z) unit Zunsat Zdeduce normalise negate  ZArithProof (fun cl => ZChecker (List.map fst cl)) f w.

(* Specifications: *)
Lemma ZTautoChecker_sound : forall f w, ZTautoChecker f w = true -> forall env, eval_bf  (Zeval_formula env)  f.
Fixpoint xhyps_of_pt (base:nat) (acc : list nat) (pt:ZArithProof)  : list nat :=
match pt with
| DoneProof => acc
| RatProof c pt => xhyps_of_pt (S base ) (xhyps_of_psatz base acc c) pt
| CutProof c pt => xhyps_of_pt (S base ) (xhyps_of_psatz base acc c) pt
| SplitProof p pt1 pt2 => xhyps_of_pt (S base) (xhyps_of_pt (S base) acc pt1) pt2
| EnumProof c1 c2 l =>
let acc := xhyps_of_psatz base (xhyps_of_psatz base acc c2) c1 in
List.fold_left (xhyps_of_pt (S base)) l acc
| ExProof _ pt  =>  xhyps_of_pt (S (S (S base ))) acc pt
end.