`BookProof.ChapterFreeFieldBornSignOrientationSubgroup.mem_orientationPreservingSigns_iff_even` (b : Fin n → Bool) : b ∈ orientationPreservingSigns n ↔ Even (flipCount b)

Proved

BookProof.ChapterFreeFieldBornSignOrientationSubgroup.mem_orientationPreservingSigns_iff_even

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignOrientationSubgroup.

BookProof.ChapterFreeFieldBornSignOrientationSubgroup.mem_orientationPreservingSigns_iff_even (b : Fin n → Bool) : b ∈ orientationPreservingSigns n ↔ Even (flipCount b)

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

Preamble

-- Generated from ChapterFreeFieldBornSignOrientationSubgroup.lean — theorem BookProof.ChapterFreeFieldBornSignOrientationSubgroup.mem_orientationPreservingSigns_iff_even
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.mem_orientationPreservingSigns_iff_even (b : Fin n → Bool) :
    b ∈ orientationPreservingSigns n ↔ Even (flipCount b) := by sorry

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