P-adic Norm not Complete on Rational Numbers/Proof 2/Lemma 1

Theorem
Let $p$ be a prime number.

Then:
 * $\exists x \in \Z_{>0}: p \nmid x, x \ge \dfrac {p + 1} 2$

Proof
Let $x = p + 1$.

Then $p \nmid x$ and:
 * $x = p + 1 > p > 0$