Definition codeSysPf : Formula := existH 1 codeSysPrf.

(* Specifications: *)
Lemma freeVarCodeSysPf : forall v : nat, In v (freeVarFormula LNN codeSysPf) -> v = 0.
Lemma codeSysPfCorrect : forall f : fol.Formula L, folProof.SysPrf L U f -> SysPrf T (substituteFormula LNN codeSysPf 0 (natToTerm (codeFormula L codeF codeR f))).