Bijection has Left and Right Inverse/Proof 3

Proof
Let $f$ be a bijection.

By definition, $f$ is a mapping, and hence also by definition a relation.

Hence the result Bijective Relation has Left and Right Inverse applies directly and so:
 * $f^{-1} \circ f = I_S$

and
 * $f \circ f^{-1} = I_T$