`BookProof.ChapterFreeFieldBornFiberStabilizer.mem_signStab_inc` {x : EuclideanSpace ℝ (Fin n)} {b : Fin n → Bool} : b ∈ signStab x ↔ ∀ k, x k ≠ 0 → b k = true

Proved

BookProof.ChapterFreeFieldBornFiberStabilizer.mem_signStab_inc

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornFiberStabilizer.

BookProof.ChapterFreeFieldBornFiberStabilizer.mem_signStab_inc {x : EuclideanSpace ℝ (Fin n)} {b : Fin n → Bool} : b ∈ signStab x ↔ ∀ k, x k ≠ 0 → b k = true

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornFiberStabilizer.mem_signStab_inc.

Replaces the unuploadable node BookProof_ChapterFreeFieldBornFiberStabilizer_mem_signStab, whose statement name is already declared inside its published definition bundle; the _inc suffix publishes the same statement as its own node.

Preamble

-- Generated from ChapterFreeFieldBornFiberStabilizer.lean — theorem BookProof.ChapterFreeFieldBornFiberStabilizer.mem_signStab_inc
import Definitions.Def_ChapterFreeFieldBorn
import Definitions.Def_ChapterFreeFieldBornQuotient
import Definitions.Def_ChapterFreeFieldBornSignGauge
import Definitions.Def_ChapterFreeFieldBornFiberCardGeneral
import Definitions.Def_ChapterFreeFieldBornFiberBounds
import Mathlib
import Definitions.Def_ChapterFreeFieldBornFiberStabilizer
open BookProof.ChapterFreeFieldBornFiberStabilizer


open MeasureTheory
open BookProof.ChapterFreeFieldBorn
open BookProof.ChapterFreeFieldBornQuotient
open BookProof.ChapterFreeFieldBornSignGauge
open BookProof.ChapterFreeFieldBornFiberCardGeneral
open BookProof.ChapterFreeFieldBornFiberBounds


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterFreeFieldBornFiberStabilizer.mem_signStab_inc {x : EuclideanSpace ℝ (Fin n)} {b : Fin n → Bool} :
    b ∈ signStab x ↔ ∀ k, x k ≠ 0 → b k = true := by sorry

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