`BookProof.ChapterFreeFieldBornSignGauge.signFlip_mem_sphere` {s : Fin n → ℝ} (hs : ∀ k, s k = 1 ∨ s k = -1) {x : EuclideanSpace ℝ (Fin n)} (hx : x ∈ Metric.sphere (0 : EuclideanSp

Proved

BookProof.ChapterFreeFieldBornSignGauge.signFlip_mem_sphere

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignGauge.

BookProof.ChapterFreeFieldBornSignGauge.signFlip_mem_sphere {s : Fin n → ℝ} (hs : ∀ k, s k = 1 ∨ s k = -1) {x : EuclideanSpace ℝ (Fin n)} (hx : x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) : signFlip s x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1

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

Preamble

-- Generated from ChapterFreeFieldBornSignGauge.lean — theorem BookProof.ChapterFreeFieldBornSignGauge.signFlip_mem_sphere
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_mem_sphere {s : Fin n → ℝ} (hs : ∀ k, s k = 1 ∨ s k = -1)
    {x : EuclideanSpace ℝ (Fin n)}
    (hx : x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) :
    signFlip s x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1 := by sorry

View graph