Inverse of Mapping is Right-Total Relation

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.

$\blacksquare$