`BookProof.ChapterFreeFieldBornSignGauge.signFlip_neg_one` (x : EuclideanSpace ℝ (Fin n)) : signFlip (fun _ => -1) x = -x

Proved

BookProof.ChapterFreeFieldBornSignGauge.signFlip_neg_one

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignGauge.

BookProof.ChapterFreeFieldBornSignGauge.signFlip_neg_one (x : EuclideanSpace ℝ (Fin n)) : signFlip (fun _ => -1) x = -x

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSignGauge.signFlip_neg_one.

Preamble

-- Generated from ChapterFreeFieldBornSignGauge.lean — theorem BookProof.ChapterFreeFieldBornSignGauge.signFlip_neg_one
import Definitions.Def_ChapterFreeFieldBorn
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSignGauge
open BookProof.ChapterFreeFieldBornSignGauge

variable {n : ℕ}


open MeasureTheory
open BookProof.ChapterFreeFieldBorn

Formal statement

theorem BookProof.ChapterFreeFieldBornSignGauge.signFlip_neg_one (x : EuclideanSpace ℝ (Fin n)) :
    signFlip (fun _ => -1) x = -x := by sorry

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