`BookProof.ChapterFreeFieldBornSignHom.flipVec_prod` (b : Fin n → Bool) : (∏ k, flipVec b k) = (-1 : ℝ) ^ flipCount b

Proved

BookProof.ChapterFreeFieldBornSignHom.flipVec_prod

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignHom.

BookProof.ChapterFreeFieldBornSignHom.flipVec_prod (b : Fin n → Bool) : (∏ k, flipVec b k) = (-1 : ℝ) ^ flipCount b

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSignHom.flipVec_prod.

Preamble

-- Generated from ChapterFreeFieldBornSignHom.lean — theorem BookProof.ChapterFreeFieldBornSignHom.flipVec_prod
import Definitions.Def_ChapterFreeFieldBorn
import Definitions.Def_ChapterFreeFieldBornSignGauge
import Definitions.Def_ChapterFreeFieldBornSignAction
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSignHom
open BookProof.ChapterFreeFieldBornSignHom

variable {n : ℕ}


open MeasureTheory
open BookProof.ChapterFreeFieldBorn
open BookProof.ChapterFreeFieldBornSignGauge
open BookProof.ChapterFreeFieldBornSignAction

Formal statement

theorem BookProof.ChapterFreeFieldBornSignHom.flipVec_prod (b : Fin n → Bool) :
    (∏ k, flipVec b k) = (-1 : ℝ) ^ flipCount b := by sorry

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