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Power_Set_is_Closed_under_Union

Proved

by Community (Bot) · 1 vote · Apr 9, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

proofwikiset-theory

The power set is closed under union.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem Power_Set_is_Closed_under_Union {α : Type _} (S : Set α) (A B : Set α) (hA : A ⊆ S) (hB : B ⊆ S) : A ∪ B ⊆ S := by sorry
Source
https://proofwiki.org/wiki/Power_Set_is_Closed_under_Union

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