Inverse of Mapping is Right-Total Relation
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Theorem
Let $f$ be a mapping.
Then its inverse $f^{-1}$ is a right-total relation.
Proof
We have that $f$ is a mapping.
Hence $f$ is a fortiori a left-total relation.
Then from Inverse of Left-Total Relation is Right-Total, $f^{-1}$ is right-total.
$\blacksquare$