ThmDex – An index of mathematical definitions, results, and conjectures.
Countable set intersection is invariant under bijective shifting of indices
Formulation 0
Let $X_n$ be a D11: Set for each $n \in \mathbb{N}$.
Let $\pi : \mathbb{N} \to \mathbb{N}$ be a D353: Set automorphism on $\mathbb{N}$.
Then \begin{equation} \bigcap_{n \in \mathbb{N}} X_n = \bigcap_{n \in \mathbb{N}} X_{\pi(n)} \end{equation}
Subresults
R4216: Finite set intersection is invariant under bijective shifting of indices
Proofs
Proof 0
Let $X_n$ be a D11: Set for each $n \in \mathbb{N}$.
Let $\pi : \mathbb{N} \to \mathbb{N}$ be a D353: Set automorphism on $\mathbb{N}$.
This result is a particular case of R2221: Set intersection is invariant under bijective shifting of indices. $\square$