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`BookProof.WeakSecondDeriv.integral_deriv_of_test` {g : ℝ → ℝ} (h : IsTestFun g) : ∫ x, deriv g x = 0

Proved
BookProof.WeakSecondDeriv.integral_deriv_of_test

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakSecondDerivative.

BookProof.WeakSecondDeriv.integral_deriv_of_test {g : ℝ → ℝ} (h : IsTestFun g) : ∫ x, deriv g x = 0

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

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



open MeasureTheory Filter Topology intervalIntegral Set

noncomputable section
Formal statement
theorem BookProof.WeakSecondDeriv.integral_deriv_of_test {g : ℝ → ℝ} (h : IsTestFun g) : ∫ x, deriv g x = 0 := by sorry

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