Composition of Sequence with Mapping

Theorem
Let $\left \langle {a_j} \right \rangle_{j \in B}$ be a sequence.

Let $\sigma: A \to B$ be a mapping, where $A \subseteq \N$.

Then $\left \langle {a_j} \right \rangle \circ \sigma$ is a sequence whose value at each $k \in A$ is $a_{\sigma \left({k}\right)}$.

Thus $\left \langle {a_j} \right \rangle \circ \sigma$ is denoted $\left \langle {a_{\sigma \left({k}\right)}} \right \rangle_{k \in A}$.