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.