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.