`BookProof.ChapterFreeFieldBornSignAction.boolFlip_free_of_pos` {b : Fin n → Bool} {x : EuclideanSpace ℝ (Fin n)} (hx : ∀ k, x k ≠ 0) : boolFlip b x = x ↔ b = (fun _ => false)

Proved

BookProof.ChapterFreeFieldBornSignAction.boolFlip_free_of_pos

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignAction.

BookProof.ChapterFreeFieldBornSignAction.boolFlip_free_of_pos {b : Fin n → Bool} {x : EuclideanSpace ℝ (Fin n)} (hx : ∀ k, x k ≠ 0) : boolFlip b x = x ↔ b = (fun _ => false)

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

Preamble

-- Generated from ChapterFreeFieldBornSignAction.lean — theorem BookProof.ChapterFreeFieldBornSignAction.boolFlip_free_of_pos
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_free_of_pos {b : Fin n → Bool} {x : EuclideanSpace ℝ (Fin n)}
    (hx : ∀ k, x k ≠ 0) :
    boolFlip b x = x ↔ b = (fun _ => false) := by sorry

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