\begin{definition}[Definition:Relation Strongly Compatible with Operation]
Let $\struct {S, \circ}$ be a closed algebraic structure.
Let $\RR$ be a relation in $S$.
Then $\RR$ is '''strongly compatible with $\circ$''' {{iff}}:
:$\forall x, y, z \in S: x \mathrel \RR y \iff \paren {x \circ z} \mathrel \RR \paren {y \circ z}$
:$\forall x, y, z \in S: x \mathrel \RR y \iff \paren {z \circ x} \mathrel \RR \paren {z \circ y}$.
That is, {{iff}} $\RR$ is compatible with $\circ$ and conversely compatible with $\circ$.
\end{definition}