Definition xnormalise (f: NFormula Z) : list (NFormula Z) :=
  let (e,o) := f in
  match o with
  | Equal     => (psub e (Pc 1),NonStrict) :: (psub (Pc (-1)) e, NonStrict) :: nil
  | NonStrict =>  ((psub (Pc (-1)) e,NonStrict)::nil)
  | Strict    =>  ((psub (Pc 0)) e, NonStrict)::nil
  | NonEqual  =>  (e, Equal)::nil
  end.

(* Specifications: *)
Lemma eval_pol_Pc : forall env z, eval_pol env (Pc z) = z.