Prove2Me

`BookProof.ChapterFreeFieldBornSignFiber.bornMap_eq_iff_signFlip` (x y : EuclideanSpace ℝ (Fin n)) : bornMap y = bornMap x ↔ ∃ s : Fin n → ℝ, (∀ k, s k = 1 ∨ s k = -1) ∧ y = signFl

Proved
BookProof.ChapterFreeFieldBornSignFiber.bornMap_eq_iff_signFlip

by leonardopedro · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignFiber.

BookProof.ChapterFreeFieldBornSignFiber.bornMap_eq_iff_signFlip (x y : EuclideanSpace ℝ (Fin n)) : bornMap y = bornMap x ↔ ∃ s : Fin n → ℝ, (∀ k, s k = 1 ∨ s k = -1) ∧ y = signFlip s x

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSignFiber.bornMap_eq_iff_signFlip.

Preamble
-- Generated from ChapterFreeFieldBornSignFiber.lean — theorem BookProof.ChapterFreeFieldBornSignFiber.bornMap_eq_iff_signFlip
import Definitions.Def_ChapterFreeFieldBorn
import Definitions.Def_ChapterFreeFieldBornSignGauge
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSignFiber
open BookProof.ChapterFreeFieldBornSignFiber

variable {n : ℕ}


open MeasureTheory
open BookProof.ChapterFreeFieldBorn BookProof.ChapterFreeFieldBornSignGauge
Formal statement
theorem BookProof.ChapterFreeFieldBornSignFiber.bornMap_eq_iff_signFlip (x y : EuclideanSpace ℝ (Fin n)) :
    bornMap y = bornMap x ↔
      ∃ s : Fin n → ℝ, (∀ k, s k = 1 ∨ s k = -1) ∧ y = signFlip s x := by sorry

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