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`BookProof.ChapterFreeFieldBornSignOrientationKernel.orientationPreserving_false` : flipMatrix (fun _ => false : Fin n → Bool) ∈ Matrix.specialOrthogonalGroup (Fin n) ℝ

Proved
BookProof.ChapterFreeFieldBornSignOrientationKernel.orientationPreserving_false

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignOrientationKernel.

BookProof.ChapterFreeFieldBornSignOrientationKernel.orientationPreserving_false : flipMatrix (fun _ => false : Fin n → Bool) ∈ Matrix.specialOrthogonalGroup (Fin n) ℝ

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSignOrientationKernel.orientationPreserving_false.

Preamble
-- Generated from ChapterFreeFieldBornSignOrientationKernel.lean — theorem BookProof.ChapterFreeFieldBornSignOrientationKernel.orientationPreserving_false
import Definitions.Def_ChapterFreeFieldBornSignHom
import Definitions.Def_ChapterFreeFieldBornSignMatrix
import Definitions.Def_ChapterFreeFieldBornSignOrientation
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSignOrientationKernel
open BookProof.ChapterFreeFieldBornSignOrientationKernel

variable {n : ℕ}


open BookProof.ChapterFreeFieldBornSignHom
open BookProof.ChapterFreeFieldBornSignMatrix
open BookProof.ChapterFreeFieldBornSignOrientation
Formal statement
theorem BookProof.ChapterFreeFieldBornSignOrientationKernel.orientationPreserving_false :
    flipMatrix (fun _ => false : Fin n → Bool) ∈
      Matrix.specialOrthogonalGroup (Fin n) ℝ := by sorry

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