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

Proved

BookProof.ChapterFreeFieldBornSignGauge.signFlip_norm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignGauge.

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

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

Preamble

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

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