`BookProof.ChapterFreeFieldSphereSupport.normalize_mem_sphere` {x : EuclideanSpace ℝ (Fin n)} (hx : x ≠ 0) : normalize x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1

Proved

BookProof.ChapterFreeFieldSphereSupport.normalize_mem_sphere

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldSphereSupport.

BookProof.ChapterFreeFieldSphereSupport.normalize_mem_sphere {x : EuclideanSpace ℝ (Fin n)} (hx : x ≠ 0) : normalize x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldSphereSupport.normalize_mem_sphere.

Preamble

-- Generated from ChapterFreeFieldSphereSupport.lean — theorem BookProof.ChapterFreeFieldSphereSupport.normalize_mem_sphere
import Definitions.Def_ChapterFreeFieldGaussian
import Definitions.Def_ChapterFreeFieldSphere
import Mathlib
import Definitions.Def_ChapterFreeFieldSphereSupport
open BookProof.ChapterFreeFieldSphereSupport

variable {n : ℕ}


open MeasureTheory ProbabilityTheory
open BookProof.ChapterFreeFieldGaussian BookProof.ChapterFreeFieldSphere

Formal statement

theorem BookProof.ChapterFreeFieldSphereSupport.normalize_mem_sphere {x : EuclideanSpace ℝ (Fin n)} (hx : x ≠ 0) :
    normalize x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1 := by sorry

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