`BookProof.ChapterFreeFieldBornSignHom.flipVec_xor` (b₁ b₂ : Fin n → Bool) : flipVec (fun k => xor (b₁ k) (b₂ k)) = flipVec b₁ * flipVec b₂

Proved

BookProof.ChapterFreeFieldBornSignHom.flipVec_xor

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignHom.

BookProof.ChapterFreeFieldBornSignHom.flipVec_xor (b₁ b₂ : Fin n → Bool) : flipVec (fun k => xor (b₁ k) (b₂ k)) = flipVec b₁ * flipVec b₂

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

Preamble

-- Generated from ChapterFreeFieldBornSignHom.lean — theorem BookProof.ChapterFreeFieldBornSignHom.flipVec_xor
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_xor (b₁ b₂ : Fin n → Bool) :
    flipVec (fun k => xor (b₁ k) (b₂ k)) = flipVec b₁ * flipVec b₂ := by sorry

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