Inverse of Injection is One-to-One Relation
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Theorem
Let $f$ be an injective mapping.
Then its inverse $f^{-1}$ is a one-to-one relation.
Proof
We are given that $f$ is an injective mapping.
Hence by definition $f$ is a one-to-one relation.
The result follows from from Inverse of One-to-One Relation is One-to-One.
$\blacksquare$