Inverse Function

Definition 1. Given any injection $f$, its converse relation $f^{-1}$ is also a function, called its inverse.

Proposition 1. For any injection $f$:

1. \[f \circ f^{-1} = \id_{\im f}.\]
2. \[f^{-1} \circ f = \id_{\dom f}.\]