`BookProof.ChapterFreeFieldSphere.normalize_comm` (L : EuclideanSpace ℝ (Fin n) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n)) (x : EuclideanSpace ℝ (Fin n)) : normalize (L x) = L (normalize x)

Proved

BookProof.ChapterFreeFieldSphere.normalize_comm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldSphere.

BookProof.ChapterFreeFieldSphere.normalize_comm (L : EuclideanSpace ℝ (Fin n) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n)) (x : EuclideanSpace ℝ (Fin n)) : normalize (L x) = L (normalize x)

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldSphere.normalize_comm.

Preamble

-- Generated from ChapterFreeFieldSphere.lean — theorem BookProof.ChapterFreeFieldSphere.normalize_comm
import Definitions.Def_ChapterFreeFieldGaussian
import Mathlib
import Definitions.Def_ChapterFreeFieldSphere
open BookProof.ChapterFreeFieldSphere

variable {n : ℕ}


open MeasureTheory
open BookProof.ChapterFreeFieldGaussian

Formal statement

theorem BookProof.ChapterFreeFieldSphere.normalize_comm (L : EuclideanSpace ℝ (Fin n) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n))
    (x : EuclideanSpace ℝ (Fin n)) : normalize (L x) = L (normalize x) := by sorry

View graph