ThmDex – An index of mathematical definitions, results, and conjectures.
Difference of set and countable union equals intersection of differences
Formulation 0
Let $X$ be a D11: Set.
Let $E_n$ be a D11: Set for each $n \in \mathbb{N}$.
Then \begin{equation} X \setminus \bigcup_{n \in \mathbb{N}} E_n = \bigcap_{n \in \mathbb{N}} (X \setminus E_n) \end{equation}
Subresults
R4172: Difference of set and finite union equals intersection of differences
Proofs
Proof 0
Let $X$ be a D11: Set.
Let $E_n$ be a D11: Set for each $n \in \mathbb{N}$.
This result is a particular case of R220: Difference of set and union equals intersection of differences. $\square$