`BookProof.ChapterFreeFieldBornSurj.bornMap_surjOn_stdSimplex` : Set.SurjOn (bornMap : EuclideanSpace ℝ (Fin n) → _) (Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) (stdSimplex ℝ

Proved

BookProof.ChapterFreeFieldBornSurj.bornMap_surjOn_stdSimplex

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSurj.

BookProof.ChapterFreeFieldBornSurj.bornMap_surjOn_stdSimplex : Set.SurjOn (bornMap : EuclideanSpace ℝ (Fin n) → _) (Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) (stdSimplex ℝ (Fin n))

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

Preamble

-- Generated from ChapterFreeFieldBornSurj.lean — theorem BookProof.ChapterFreeFieldBornSurj.bornMap_surjOn_stdSimplex
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.bornMap_surjOn_stdSimplex :
    Set.SurjOn (bornMap : EuclideanSpace ℝ (Fin n) → _)
      (Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) (stdSimplex ℝ (Fin n)) := by sorry

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