`BookProof.ChapterFreeFieldBornSignOrientationSubgroup.orientationPreservingSigns_index` (n : ℕ) : (orientationPreservingSigns (n + 1)).index = 2

Proved

BookProof.ChapterFreeFieldBornSignOrientationSubgroup.orientationPreservingSigns_index

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignOrientationSubgroup.

BookProof.ChapterFreeFieldBornSignOrientationSubgroup.orientationPreservingSigns_index (n : ℕ) : (orientationPreservingSigns (n + 1)).index = 2

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSignOrientationSubgroup.orientationPreservingSigns_index.

Preamble

-- Generated from ChapterFreeFieldBornSignOrientationSubgroup.lean — theorem BookProof.ChapterFreeFieldBornSignOrientationSubgroup.orientationPreservingSigns_index
import Definitions.Def_ChapterFreeFieldBornSignHom
import Definitions.Def_ChapterFreeFieldBornSignMatrix
import Definitions.Def_ChapterFreeFieldBornSignOrientation
import Definitions.Def_ChapterFreeFieldBornSignOrientationKernel
import Definitions.Def_ChapterFreeFieldBornSignOrientationCard
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSignOrientationSubgroup
open BookProof.ChapterFreeFieldBornSignOrientationSubgroup

variable {n : ℕ}


open BookProof.ChapterFreeFieldBornSignHom
open BookProof.ChapterFreeFieldBornSignMatrix
open BookProof.ChapterFreeFieldBornSignOrientation
open BookProof.ChapterFreeFieldBornSignOrientationKernel
open BookProof.ChapterFreeFieldBornSignOrientationCard

Formal statement

theorem BookProof.ChapterFreeFieldBornSignOrientationSubgroup.orientationPreservingSigns_index (n : ℕ) :
    (orientationPreservingSigns (n + 1)).index = 2 := by sorry

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