(related to Lemma: Composition of Functions)

- By hypothesis, \(f:A\mapsto B\) and \(g:B\mapsto C\) are functions.
- Let $f\subseteq A\times B$ and $g\subseteq B\times C$ be the corresponding corresponding relations.
- Let $g\circ f\subseteq A\times C$ be the composition of these relations.
- We have already shown that $g\circ f$ is right-unique.
- We have already shown that $g\circ f$ is left-total.
- By definition of a function, $g\circ f$ is a function.∎

**Knauer Ulrich**: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001