General Positivity Rule in Ordered Integral Domain/Corollary

Corollary to General Positivity Rule in Ordered Integral Domain
Let $\left({D, +, \times}\right)$ be an ordered integral domain, whose positivity property is denoted $P$.

Let $P \left({x}\right)$ where $x \in D$.

Then:
 * $P \left({n \cdot x}\right)$ and $P \left({x^n}\right)$

Proof
From the definition of power of an element:
 * $\displaystyle n \cdot x = \sum_{i \mathop = 1}^n x$


 * $\displaystyle x^n = \prod_{i \mathop = 1}^n x$

The result then follows directly from [[General Positivity Rule in Ordered Integral Domain].