Relations Compatible with Group Form Complete Boolean Algebra

Theorem

Let $\struct {S, \circ}$ be a group.

Let $C$ be the set of relations on $S$ which are compatible with $\circ$.

Then $\struct {C, \cap, \cup, \subseteq}$ is a complete Boolean lattice.

Proof

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.