`BookProof.ChapterFreeFieldBornSignFiber.signFlip_comp` (s t : Fin n → ℝ) (x : EuclideanSpace ℝ (Fin n)) : signFlip s (signFlip t x) = signFlip (fun k => s k * t k) x

Proved

BookProof.ChapterFreeFieldBornSignFiber.signFlip_comp

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignFiber.

BookProof.ChapterFreeFieldBornSignFiber.signFlip_comp (s t : Fin n → ℝ) (x : EuclideanSpace ℝ (Fin n)) : signFlip s (signFlip t x) = signFlip (fun k => s k * t k) x

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

Preamble

-- Generated from ChapterFreeFieldBornSignFiber.lean — theorem BookProof.ChapterFreeFieldBornSignFiber.signFlip_comp
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.signFlip_comp (s t : Fin n → ℝ) (x : EuclideanSpace ℝ (Fin n)) :
    signFlip s (signFlip t x) = signFlip (fun k => s k * t k) x := by sorry

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