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

Proved

BookProof.ChapterFreeFieldBornFiberStabilizer.signStab_card_mul_two_pow_nonzero

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornFiberStabilizer.

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

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

Preamble

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

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