Definition codeFormula := codeFormula LNT codeLNTFunction codeLNTRelation.Definition T' : fol.System LNN :=
  Union _ NN
    (fun x : fol.Formula LNN => mem _ T (LNN2LNT_formula x)).

Lemma Tprf2T'prf : forall f : Formula, SysPrf T f -> folProof.SysPrf LNN T' (LNT2LNN_formula f).