I proved the following two similar theorems about funcoids and reloids:

**Theorem**

- For a complete funcoid there exist exactly one function

such that

. - For a co-complete funcoid there exist exactly one function

such that

.

**Theorem**

- For a complete reloid there exist exactly one function

such that

. - For a co-complete reloid there exist exactly one function

such that

.

See this online article for definitions of used concepts and proofs.