Let $f : X \to X$ be a D2660: Set endomorphism such that
(i) | $E \subseteq X$ is a D78: Subset of $X$ |
(ii) | $I_E : X \to \{ 0, 1 \}$ is the D41: Indicator function of $E$ within $X$ |
Then
\begin{equation}
I_E \circ f
= I_{f^{-1}(E)}
\end{equation}