Inverse of Mapping is One-to-Many Relation

Theorem
Let $f$ be a mapping.

Then its inverse $f^{-1}$ is a one-to-many relation.

Proof
As $f$, being a mapping, is necessarily a many-to-one relation, then from Inverse of Many-to-One Relation is One-to-Many, $f^{-1}$ is one-to-many.