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:


 * $\displaystyle \mathcal R^{-1} \sqbrk {\bigcup_{i \mathop \in I} T_i} = \bigcup_{i \mathop \in I} \mathcal R^{-1} \sqbrk {T_i}$

where $\mathcal R^{-1} \sqbrk {T_i}$ denotes the preimage of $T_i$ under $\mathcal R^{-1}$.