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

(* Specifications: *)
Lemma extendsNN : Included _ NN T'.
Lemma freeVarRepT' : forall v : nat, In v (freeVarFormula LNN (LNT2LNN_formula repT)) -> v = v0.
Lemma Tprf2T'prf : forall f : Formula, SysPrf T f -> folProof.SysPrf LNN T' (LNT2LNN_formula f).
Lemma expressT'1 : forall f : Formula, mem _ T f -> folProof.SysPrf LNN T' (substituteFormula LNN (LNT2LNN_formula repT) v0 (natToTermLNN (codeFormula f))).
Lemma expressT'2 : forall f : Formula, ~ mem _ T f -> folProof.SysPrf LNN T' (fol.notH LNN (substituteFormula LNN (LNT2LNN_formula repT) v0 (natToTermLNN (codeFormula f)))).