`BookProof.ChapterFreeFieldBornCont.stdSimplex_eq_bornMap_image_sphere` : stdSimplex ℝ (Fin n) = (bornMap : EuclideanSpace ℝ (Fin n) → (Fin n → ℝ)) '' (Metric.sphere (0 : Euclidean

Proved

BookProof.ChapterFreeFieldBornCont.stdSimplex_eq_bornMap_image_sphere

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornCont.

BookProof.ChapterFreeFieldBornCont.stdSimplex_eq_bornMap_image_sphere : stdSimplex ℝ (Fin n) = (bornMap : EuclideanSpace ℝ (Fin n) → (Fin n → ℝ)) '' (Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1)

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornCont.stdSimplex_eq_bornMap_image_sphere.

Preamble

-- Generated from ChapterFreeFieldBornCont.lean — theorem BookProof.ChapterFreeFieldBornCont.stdSimplex_eq_bornMap_image_sphere
import Definitions.Def_ChapterFreeFieldBorn
import Definitions.Def_ChapterFreeFieldBornSurj
import Mathlib
import Definitions.Def_ChapterFreeFieldBornCont
open BookProof.ChapterFreeFieldBornCont

variable {n : ℕ}


open MeasureTheory
open BookProof.ChapterFreeFieldBorn BookProof.ChapterFreeFieldBornSurj

Formal statement

theorem BookProof.ChapterFreeFieldBornCont.stdSimplex_eq_bornMap_image_sphere :
    stdSimplex ℝ (Fin n) =
      (bornMap : EuclideanSpace ℝ (Fin n) → (Fin n → ℝ)) ''
        (Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) := by sorry

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