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