`BookProof.ChapterFreeFieldBornSignAction.boolFlip_mem_sphere` (b : Fin n → Bool) {x : EuclideanSpace ℝ (Fin n)} (hx : x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) : boolFli

Proved

BookProof.ChapterFreeFieldBornSignAction.boolFlip_mem_sphere

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignAction.

BookProof.ChapterFreeFieldBornSignAction.boolFlip_mem_sphere (b : Fin n → Bool) {x : EuclideanSpace ℝ (Fin n)} (hx : x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) : boolFlip b x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSignAction.boolFlip_mem_sphere.

Preamble

-- Generated from ChapterFreeFieldBornSignAction.lean — theorem BookProof.ChapterFreeFieldBornSignAction.boolFlip_mem_sphere
import Definitions.Def_ChapterFreeFieldBorn
import Definitions.Def_ChapterFreeFieldBornSignGauge
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSignAction
open BookProof.ChapterFreeFieldBornSignAction

variable {n : ℕ}


open MeasureTheory
open BookProof.ChapterFreeFieldBorn
open BookProof.ChapterFreeFieldBornSignGauge

Formal statement

theorem BookProof.ChapterFreeFieldBornSignAction.boolFlip_mem_sphere (b : Fin n → Bool) {x : EuclideanSpace ℝ (Fin n)}
    (hx : x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) :
    boolFlip b x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1 := by sorry

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