Upper bound on the cardinality of an arbitrary union

Let ${𝐴 𝑘} 𝑘 \in 𝐾$ be a collection of sets such that $| 𝐴 𝑘 | \leq 𝜆$ for all $𝑘 \in 𝐾$ and $| 𝐾 | = 𝜅$ . Then¹ #m/thm/set

∣ ⋃ 𝑘 \in 𝐾 𝐴 𝑘 ∣ \leq 𝜆 𝜅

Proof

#missing/proof

#state/develop | #lang/en | #SemBr

Footnotes