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

Theorem
Let $p$ be a prime number.

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

Proof
Let $x = p + 1$

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