`BookProof.ChapterFreeFieldBornSignOrientationSubgroup.sub_mem_orientationPreservingSigns_iff` (b₁ b₂ : Fin n → Bool) : b₁ - b₂ ∈ orientationPreservingSigns n ↔ (b₁ ∈ orientationPr

Proved

BookProof.ChapterFreeFieldBornSignOrientationSubgroup.sub_mem_orientationPreservingSigns_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignOrientationSubgroup.

BookProof.ChapterFreeFieldBornSignOrientationSubgroup.sub_mem_orientationPreservingSigns_iff (b₁ b₂ : Fin n → Bool) : b₁ - b₂ ∈ orientationPreservingSigns n ↔ (b₁ ∈ orientationPreservingSigns n ↔ b₂ ∈ orientationPreservingSigns n)

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

Preamble

-- Generated from ChapterFreeFieldBornSignOrientationSubgroup.lean — theorem BookProof.ChapterFreeFieldBornSignOrientationSubgroup.sub_mem_orientationPreservingSigns_iff
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.sub_mem_orientationPreservingSigns_iff (b₁ b₂ : Fin n → Bool) :
    b₁ - b₂ ∈ orientationPreservingSigns n ↔
      (b₁ ∈ orientationPreservingSigns n ↔
       b₂ ∈ orientationPreservingSigns n) := by sorry

View graph