Direct Image Mapping is Bijection iff Mapping is Bijection

Theorem

Let $\RR \subseteq S \times T$ be a relation.

Let $\RR^\to: \powerset S \to \powerset T$ be the direct image mapping of $\RR$.

Then $\RR \subseteq S \times T$ is a bijection if and only if $\RR^\to: \powerset S \to \powerset T$ is a bijection.

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.