Prove2Me

`BookProof.ChapterFreeFieldBornSectionBij.mem_nonnegOrthant` {x : EuclideanSpace ℝ (Fin n)} : x ∈ nonnegOrthant n ↔ ∀ k, 0 ≤ x k

Proved
BookProof.ChapterFreeFieldBornSectionBij.mem_nonnegOrthant

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSectionBij.

BookProof.ChapterFreeFieldBornSectionBij.mem_nonnegOrthant {x : EuclideanSpace ℝ (Fin n)} : x ∈ nonnegOrthant n ↔ ∀ k, 0 ≤ x k

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

Preamble
-- Generated from ChapterFreeFieldBornSectionBij.lean — theorem BookProof.ChapterFreeFieldBornSectionBij.mem_nonnegOrthant
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.mem_nonnegOrthant {x : EuclideanSpace ℝ (Fin n)} :
    x ∈ nonnegOrthant n ↔ ∀ k, 0 ≤ x k := by sorry

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