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

Proved

BookProof.ChapterFreeFieldBornSignGauge.bornMap_signFlip

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignGauge.

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

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

Preamble

-- Generated from ChapterFreeFieldBornSignGauge.lean — theorem BookProof.ChapterFreeFieldBornSignGauge.bornMap_signFlip
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.bornMap_signFlip {s : Fin n → ℝ} (hs : ∀ k, s k = 1 ∨ s k = -1)
    (x : EuclideanSpace ℝ (Fin n)) :
    bornMap (signFlip s x) = bornMap x := by sorry

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