Let $X \neq \emptyset$ be a D11: Set.
Let $f : X \to Y$ be a D18: Map.
Let ${\sim}_f \subseteq X \times X$ be the D184: Constancy relation on $X$ with respect to $f$.
The constancy class of $x \in X$ with respect to $f$ is the D11: Set \begin{equation} {\sim}_f(x) : = \{ y \mid (x, y) \in {\sim}_f \} \end{equation}

Let $X \neq \emptyset$ be a D11: Set.
Let $f : X \to Y$ be a D18: Map.
The constancy class of $x \in X$ with respect to $f$ is the D11: Set \begin{equation} {\sim}_f(x) : = \{ y \mid f(x) = f(y) \} \end{equation}