`BookProof.ChapterFreeFieldBornSectionBij.bornSection_bornMap` {x : EuclideanSpace ℝ (Fin n)} (hx : x ∈ nonnegOrthant n) : bornSection (bornMap x) = x

Proved

BookProof.ChapterFreeFieldBornSectionBij.bornSection_bornMap

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSectionBij.

BookProof.ChapterFreeFieldBornSectionBij.bornSection_bornMap {x : EuclideanSpace ℝ (Fin n)} (hx : x ∈ nonnegOrthant n) : bornSection (bornMap x) = x

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSectionBij.bornSection_bornMap.

Preamble

-- Generated from ChapterFreeFieldBornSectionBij.lean — theorem BookProof.ChapterFreeFieldBornSectionBij.bornSection_bornMap
import Definitions.Def_ChapterFreeFieldGaussian
import Definitions.Def_ChapterFreeFieldSphere
import Definitions.Def_ChapterFreeFieldSphereSupport
import Definitions.Def_ChapterFreeFieldBorn
import Definitions.Def_ChapterFreeFieldBornSurj
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSectionBij
open BookProof.ChapterFreeFieldBornSectionBij

variable {n : ℕ}


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

Formal statement

theorem BookProof.ChapterFreeFieldBornSectionBij.bornSection_bornMap {x : EuclideanSpace ℝ (Fin n)} (hx : x ∈ nonnegOrthant n) :
    bornSection (bornMap x) = x := by sorry

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