Strictly_Increasing_Sequence_of_Natural_Numbers

Let $\N_{>0}$ be the set of natural numbers without zero $\N_{>0} = \left\{{1, 2, 3, \ldots}\right\}$ Let $\left \langle {n_r} \right \rangle$ be strictly increasing sequence in $\N_{>0}$. Then $\forall r \in \N_{>0}: n_r \ge r$