`BookProof.WeakSecondDeriv.exists_antideriv` {g : ℝ → ℝ} (h : IsTestFun g) (h0 : ∫ x, g x = 0) : ∃ G : ℝ → ℝ, IsTestFun G ∧ deriv G = g

Proved

BookProof.WeakSecondDeriv.exists_antideriv

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakSecondDerivative.

BookProof.WeakSecondDeriv.exists_antideriv {g : ℝ → ℝ} (h : IsTestFun g) (h0 : ∫ x, g x = 0) : ∃ G : ℝ → ℝ, IsTestFun G ∧ deriv G = g

Formalization note: Lean 4 identifier BookProof.WeakSecondDeriv.exists_antideriv.

Preamble

-- Generated from ChapterWeakSecondDerivative.lean — theorem BookProof.WeakSecondDeriv.exists_antideriv
import Mathlib
import Definitions.Def_ChapterWeakSecondDerivative
open BookProof.WeakSecondDeriv



open MeasureTheory Filter Topology intervalIntegral Set

noncomputable section

Formal statement

theorem BookProof.WeakSecondDeriv.exists_antideriv {g : ℝ → ℝ} (h : IsTestFun g) (h0 : ∫ x, g x = 0) :
    ∃ G : ℝ → ℝ, IsTestFun G ∧ deriv G = g := by sorry

View graph