Definition:Relation Conversely Compatible with Operation

Definition
Let $\struct {S, \circ}$ be a closed algebraic structure.

Let $\RR$ be a relation in $S$.

Then $\RR$ is conversely compatible with $\circ$ :


 * $\forall x, y, z \in S: \paren {x \circ z} \mathrel \RR \paren {y \circ z} \implies x \mathrel \RR y$


 * $\forall x, y, z \in S: \paren {z \circ x} \mathrel \RR \paren {z \circ y} \implies x \mathrel \RR y$