`BookProof.ChapterFreeFieldBornFiberStabilizer.signStab_card` (x : EuclideanSpace ℝ (Fin n)) : (signStab x).card = 2 ^ (Finset.univ.filter (fun k => x k = 0)).card

Proved

BookProof.ChapterFreeFieldBornFiberStabilizer.signStab_card

by leonardopedro · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornFiberStabilizer.

BookProof.ChapterFreeFieldBornFiberStabilizer.signStab_card (x : EuclideanSpace ℝ (Fin n)) : (signStab x).card = 2 ^ (Finset.univ.filter (fun k => x k = 0)).card

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

Preamble

-- Generated from ChapterFreeFieldBornFiberStabilizer.lean — theorem BookProof.ChapterFreeFieldBornFiberStabilizer.signStab_card
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.signStab_card (x : EuclideanSpace ℝ (Fin n)) :
    (signStab x).card = 2 ^ (Finset.univ.filter (fun k => x k = 0)).card := by sorry

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