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No_Bijection_from_Set_to_its_Power_Set

Proved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

bijectionspower-setproofwiki

Let S be a set. There is no bijection f: S → 𝒫(S).

Preamble
import Mathlib.Data.Set.Basic
import Mathlib.Logic.Function.Basic
Formal statement
theorem No_Bijection_from_Set_to_its_Power_Set {α : Type _} (f : α → Set α) : ¬ Function.Bijective f := by sorry
Source
https://proofwiki.org/wiki/No_Bijection_from_Set_to_its_Power_Set

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