`BookProof.ChapterFreeFieldBornSignMatrix.flipMatrix_xor` (b₁ b₂ : Fin n → Bool) : flipMatrix (fun k => xor (b₁ k) (b₂ k)) = flipMatrix b₁ * flipMatrix b₂

Proved

BookProof.ChapterFreeFieldBornSignMatrix.flipMatrix_xor

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignMatrix.

BookProof.ChapterFreeFieldBornSignMatrix.flipMatrix_xor (b₁ b₂ : Fin n → Bool) : flipMatrix (fun k => xor (b₁ k) (b₂ k)) = flipMatrix b₁ * flipMatrix b₂

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSignMatrix.flipMatrix_xor.

Preamble

-- Generated from ChapterFreeFieldBornSignMatrix.lean — theorem BookProof.ChapterFreeFieldBornSignMatrix.flipMatrix_xor
import Definitions.Def_ChapterFreeFieldBornSignAction
import Definitions.Def_ChapterFreeFieldBornSignHom
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSignMatrix
open BookProof.ChapterFreeFieldBornSignMatrix

variable {n : ℕ}


open BookProof.ChapterFreeFieldBornSignAction
open BookProof.ChapterFreeFieldBornSignHom

Formal statement

theorem BookProof.ChapterFreeFieldBornSignMatrix.flipMatrix_xor (b₁ b₂ : Fin n → Bool) :
    flipMatrix (fun k => xor (b₁ k) (b₂ k)) = flipMatrix b₁ * flipMatrix b₂ := by sorry

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