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Proof

(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.
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References

Bibliography

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