`BookProof.ChapterFreeFieldBornSignMatrix.det_flipMatrix` (b : Fin n → Bool) : Matrix.det (flipMatrix b) = (-1 : ℝ) ^ flipCount b

Proved

BookProof.ChapterFreeFieldBornSignMatrix.det_flipMatrix

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignMatrix.

BookProof.ChapterFreeFieldBornSignMatrix.det_flipMatrix (b : Fin n → Bool) : Matrix.det (flipMatrix b) = (-1 : ℝ) ^ flipCount b

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

Preamble

-- Generated from ChapterFreeFieldBornSignMatrix.lean — theorem BookProof.ChapterFreeFieldBornSignMatrix.det_flipMatrix
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.det_flipMatrix (b : Fin n → Bool) :
    Matrix.det (flipMatrix b) = (-1 : ℝ) ^ flipCount b := by sorry

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