ThmDex – An index of mathematical definitions, results, and conjectures.

Result R2222 on D77: Set union

Set union is invariant under bijective shifting of indices

Formulation 0

Let $X_j$ be a D11: Set for each $j \in J$.
Let $\pi : J \to J$ be a D353: Set automorphism on $J$.

Then \begin{equation} \bigcup_{j \in J} X_j = \bigcup_{j \in J} X_{\pi(j)} \end{equation}