`BookProof.ChapterFreeFieldBornSignMatrix.flipMatrix_mulVec` (b : Fin n → Bool) (x : EuclideanSpace ℝ (Fin n)) : (flipMatrix b).mulVec x = boolFlip b x

Proved

BookProof.ChapterFreeFieldBornSignMatrix.flipMatrix_mulVec

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignMatrix.

BookProof.ChapterFreeFieldBornSignMatrix.flipMatrix_mulVec (b : Fin n → Bool) (x : EuclideanSpace ℝ (Fin n)) : (flipMatrix b).mulVec x = boolFlip b x

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

Preamble

-- Generated from ChapterFreeFieldBornSignMatrix.lean — theorem BookProof.ChapterFreeFieldBornSignMatrix.flipMatrix_mulVec
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_mulVec (b : Fin n → Bool) (x : EuclideanSpace ℝ (Fin n)) :
    (flipMatrix b).mulVec x = boolFlip b x := by sorry

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