`BookProof.ChapterFreeFieldSphere.sphereGaussian_map_linearIsometryEquiv` (L : EuclideanSpace ℝ (Fin n) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n)) : (sphereGaussian n).map L = sphereGaussian

Proved

BookProof.ChapterFreeFieldSphere.sphereGaussian_map_linearIsometryEquiv

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldSphere.

BookProof.ChapterFreeFieldSphere.sphereGaussian_map_linearIsometryEquiv (L : EuclideanSpace ℝ (Fin n) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n)) : (sphereGaussian n).map L = sphereGaussian n

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

Preamble

-- Generated from ChapterFreeFieldSphere.lean — theorem BookProof.ChapterFreeFieldSphere.sphereGaussian_map_linearIsometryEquiv
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.sphereGaussian_map_linearIsometryEquiv
    (L : EuclideanSpace ℝ (Fin n) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n)) :
    (sphereGaussian n).map L = sphereGaussian n := by sorry

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