`BookProof.ChapterFreeFieldBorn.bornMap_sum_of_mem_sphere` {x : EuclideanSpace ℝ (Fin n)} (hx : x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) : ∑ k, bornMap x k = 1

Proved

BookProof.ChapterFreeFieldBorn.bornMap_sum_of_mem_sphere

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBorn.

BookProof.ChapterFreeFieldBorn.bornMap_sum_of_mem_sphere {x : EuclideanSpace ℝ (Fin n)} (hx : x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) : ∑ k, bornMap x k = 1

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBorn.bornMap_sum_of_mem_sphere.

Preamble

-- Generated from ChapterFreeFieldBorn.lean — theorem BookProof.ChapterFreeFieldBorn.bornMap_sum_of_mem_sphere
import Definitions.Def_ChapterFreeFieldGaussian
import Definitions.Def_ChapterFreeFieldSphere
import Definitions.Def_ChapterFreeFieldSphereSupport
import Mathlib
import Definitions.Def_ChapterFreeFieldBorn
open BookProof.ChapterFreeFieldBorn

variable {n : ℕ}


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

Formal statement

theorem BookProof.ChapterFreeFieldBorn.bornMap_sum_of_mem_sphere {x : EuclideanSpace ℝ (Fin n)}
    (hx : x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) :
    ∑ k, bornMap x k = 1 := by sorry

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