Translation of Index Variable of Summation/Infinite Series

Theorem
Let $R: \Z \to \left\{ {\mathrm T, \mathrm F}\right\}$ be a propositional function on the set of integers.

Let $\displaystyle \sum_{R \left({j}\right)} a_j$ denote a summation over $R$.

Let the fiber of truth of $R$ be infinite.

Then:
 * $\displaystyle \sum_{R \left({j}\right)} a_j = \sum_{R \left({c \mathop + j}\right)} a_{c \mathop + j} = \sum_{R \left({c \mathop - j}\right)} a_{c \mathop - j}$

where $c$ is an integer constant which is not dependent upon $j$.