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Set_Complement_inverts_Subsets

Proved

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

proofwikiset-complementsubsets

S is a subset of T if and only if the complement of T is a subset of the complement of S.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
import Mathlib.Analysis.Complex.Basic

theorem Set_Complement_inverts_Subsets {alpha : Type _} (S T : Set alpha) :
  S <= T <-> T.compl <= S.compl := by sorry
Source
https://proofwiki.org/wiki/Set_Complement_inverts_Subsets

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