(** Another normalisation - this is used for cnf conversion **)
Definition xnormalise (f:NFormula) : list (NFormula)  :=
let (e,o) := f in
match o with
| Equal     => (e , Strict) :: (popp e, Strict) :: nil
| NonEqual  => (e , Equal) :: nil
| Strict    => (popp e, NonStrict) :: nil
| NonStrict => (popp e, Strict) :: nil
end.
Definition xnegate (t:NFormula) : list (NFormula)  :=
let (e,o) := t in
match o with
| Equal  => (e,Equal) :: nil
| NonEqual => (e,Strict)::(popp e,Strict)::nil
| Strict  => (e,Strict) :: nil
| NonStrict  => (e,NonStrict) :: nil
end.
Definition cnf_of_list {T : Type} (l:list NFormula) (tg : T) : cnf NFormula T :=
List.fold_right (fun x acc =>
if check_inconsistent x then acc else ((x,tg)::nil)::acc)
(cnf_tt _ _)  l.
Add Ring SORRing : (SORrt sor).

Lemma cnf_of_list_correct :
forall (T : Type) env l tg,
eval_cnf (Annot:=T) eval_nformula env (cnf_of_list l tg) <->
make_conj (fun x : NFormula => eval_nformula env x -> False) l.