Definition ZweakTautoChecker (w: list ZWitness) (f : BFormula (Formula Z) Tauto.isProp) : bool :=
@tauto_checker (Formula Z)  (NFormula Z) unit Zunsat Zdeduce normalise negate  ZWitness (fun cl => ZWeakChecker (List.map fst cl)) f w.
(* To get a complete checker, the proof format has to be enriched *)
Local Open Scope Z_scope.
Definition ceiling (a b:Z) : Z :=
let (q,r) := Z.div_eucl a b in
match r with
| Z0 => q
| _  => q + 1
end.

Lemma narrow_interval_lower_bound a b x :
a > 0 -> a * x  >= b -> x >= ceiling b a.