Definition check_normalised_formulas : list NFormula -> Psatz -> bool :=
  fun l cm =>
    match eval_Psatz l cm with
      | None => false
      | Some f => check_inconsistent f
    end.

Lemma checker_nf_sound : forall (l : list NFormula) (cm : Psatz), check_normalised_formulas l cm = true -> forall env : PolEnv, make_impl (eval_nformula env) l False.