Power Function on Base between Zero and One is Strictly Decreasing/Integer

Theorem
Let $a \in \R$.

Let $0 < a < 1$.

Let $f : \Z \to \R$ be the real mapping defined as:
 * $f \left({ k }\right) = a^n$

where $a^k$ denotes $a$ to the power of $k$.

Then $f$ is strictly decreasing.

Proof
By Exponential with Base Between Zero and One is Strictly Decreasing/Natural Number, the theorem is already proven for positive integers.

Let $i, j$ be integers such that $i < j < 0$.

Hence the result.