`BookProof.ChapterFreeFieldBornSurj.bornSection_mem_sphere` {p : Fin n → ℝ} (hp : p ∈ stdSimplex ℝ (Fin n)) : bornSection p ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1

Proved

BookProof.ChapterFreeFieldBornSurj.bornSection_mem_sphere

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSurj.

BookProof.ChapterFreeFieldBornSurj.bornSection_mem_sphere {p : Fin n → ℝ} (hp : p ∈ stdSimplex ℝ (Fin n)) : bornSection p ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSurj.bornSection_mem_sphere.

Preamble

-- Generated from ChapterFreeFieldBornSurj.lean — theorem BookProof.ChapterFreeFieldBornSurj.bornSection_mem_sphere
import Definitions.Def_ChapterFreeFieldGaussian
import Definitions.Def_ChapterFreeFieldSphere
import Definitions.Def_ChapterFreeFieldSphereSupport
import Definitions.Def_ChapterFreeFieldBorn
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSurj
open BookProof.ChapterFreeFieldBornSurj

variable {n : ℕ}


open MeasureTheory
open BookProof.ChapterFreeFieldGaussian BookProof.ChapterFreeFieldSphere
open BookProof.ChapterFreeFieldSphereSupport BookProof.ChapterFreeFieldBorn

Formal statement

theorem BookProof.ChapterFreeFieldBornSurj.bornSection_mem_sphere {p : Fin n → ℝ} (hp : p ∈ stdSimplex ℝ (Fin n)) :
    bornSection p ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1 := by sorry

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