Lemma PAboundedLT : forall (m : nat) (a : Formula) (x : nat), (forall n : nat, n < m -> SysPrf PA (substituteFormula LNT a x (natToTerm n))) -> SysPrf PA (impH (LNN2LNT_formula (LT (fol.var LNN x) (LNN.natToTerm m))) a).