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.

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