Definition cnf_normalise {T: Type} (t: Formula C) (tg: T) : cnf NFormula T :=
  let f := normalise t in
  if check_inconsistent f then cnf_ff _ _
  else cnf_of_list (xnormalise f) tg.Definition cnf_negate {T: Type} (t: Formula C) (tg: T) : cnf NFormula T :=
  let f := normalise t in
  if check_inconsistent f then cnf_tt _ _
  else cnf_of_list (xnegate f) tg.

Lemma xnegate_correct : forall env f, (make_conj (fun x => eval_nformula env x -> False) (xnegate f)) <-> ~ eval_nformula env f.