`BookProof.ChapterFreeFieldBornSignFiber.signFlip_involutive` {s : Fin n → ℝ} (hs : ∀ k, s k = 1 ∨ s k = -1) (x : EuclideanSpace ℝ (Fin n)) : signFlip s (signFlip s x) = x

Proved

BookProof.ChapterFreeFieldBornSignFiber.signFlip_involutive

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignFiber.

BookProof.ChapterFreeFieldBornSignFiber.signFlip_involutive {s : Fin n → ℝ} (hs : ∀ k, s k = 1 ∨ s k = -1) (x : EuclideanSpace ℝ (Fin n)) : signFlip s (signFlip s x) = x

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSignFiber.signFlip_involutive.

Preamble

-- Generated from ChapterFreeFieldBornSignFiber.lean — theorem BookProof.ChapterFreeFieldBornSignFiber.signFlip_involutive
import Definitions.Def_ChapterFreeFieldBorn
import Definitions.Def_ChapterFreeFieldBornSignGauge
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSignFiber
open BookProof.ChapterFreeFieldBornSignFiber

variable {n : ℕ}


open MeasureTheory
open BookProof.ChapterFreeFieldBorn BookProof.ChapterFreeFieldBornSignGauge

Formal statement

theorem BookProof.ChapterFreeFieldBornSignFiber.signFlip_involutive {s : Fin n → ℝ} (hs : ∀ k, s k = 1 ∨ s k = -1)
    (x : EuclideanSpace ℝ (Fin n)) :
    signFlip s (signFlip s x) = x := by sorry

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