`BookProof.ChapterFreeFieldBornSignAction.boolFlip_involutive` (b : Fin n → Bool) (x : EuclideanSpace ℝ (Fin n)) : boolFlip b (boolFlip b x) = x

Proved

BookProof.ChapterFreeFieldBornSignAction.boolFlip_involutive

by leonardopedro · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignAction.

BookProof.ChapterFreeFieldBornSignAction.boolFlip_involutive (b : Fin n → Bool) (x : EuclideanSpace ℝ (Fin n)) : boolFlip b (boolFlip b x) = x

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSignAction.boolFlip_involutive.

Preamble

-- Generated from ChapterFreeFieldBornSignAction.lean — theorem BookProof.ChapterFreeFieldBornSignAction.boolFlip_involutive
import Definitions.Def_ChapterFreeFieldBorn
import Definitions.Def_ChapterFreeFieldBornSignGauge
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSignAction
open BookProof.ChapterFreeFieldBornSignAction

variable {n : ℕ}


open MeasureTheory
open BookProof.ChapterFreeFieldBorn
open BookProof.ChapterFreeFieldBornSignGauge

Formal statement

theorem BookProof.ChapterFreeFieldBornSignAction.boolFlip_involutive (b : Fin n → Bool) (x : EuclideanSpace ℝ (Fin n)) :
    boolFlip b (boolFlip b x) = x := by sorry

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