Preimage of Union under Mapping/Family of Sets/Proof 1

Proof
As $f$, being a mapping, is also a relation, we can apply Preimage of Union under Relation: Family of Sets:


 * $\displaystyle \mathcal R^{-1} \left[{\bigcup_{i \mathop \in I} T_i}\right] = \bigcup_{i \mathop \in I} \mathcal R^{-1} \left[{T_i}\right]$

where $\mathcal R^{-1} \left[{T_i}\right]$ denotes the preimage of $T_i$ under $\mathcal R^{-1}$.