Require Export LNN2LNT.

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).