`BookProof.WeylCauchyRiemann.mollify_moll_eq_self` {h : ℂ → ℂ} {s : Set ℂ} (hs : IsOpen s) (hh : DifferentiableOn ℂ h s) (hcont : Continuous h) {δ : ℝ} (hδ : 0 < δ) {z : ℂ} (hz : c

Proved

BookProof.WeylCauchyRiemann.mollify_moll_eq_self

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylCauchyRiemann.

BookProof.WeylCauchyRiemann.mollify_moll_eq_self {h : ℂ → ℂ} {s : Set ℂ} (hs : IsOpen s) (hh : DifferentiableOn ℂ h s) (hcont : Continuous h) {δ : ℝ} (hδ : 0 < δ) {z : ℂ} (hz : closedBall z δ ⊆ s) : mollify h (moll δ) z = h z

Formalization note: Lean 4 identifier BookProof.WeylCauchyRiemann.mollify_moll_eq_self.

Preamble

-- Generated from ChapterWeylCauchyRiemann.lean — theorem BookProof.WeylCauchyRiemann.mollify_moll_eq_self
import Mathlib
import Definitions.Def_ChapterWeylCauchyRiemann
import Definitions.Def_ChapterRadialMollifier
open BookProof.RadialMollifier
open BookProof.WeylCauchyRiemann



open MeasureTheory Metric Set Filter Complex BookProof.RadialMollifier
open scoped Convolution Topology ContDiff

noncomputable section

Formal statement

theorem BookProof.WeylCauchyRiemann.mollify_moll_eq_self {h : ℂ → ℂ} {s : Set ℂ} (hs : IsOpen s)
    (hh : DifferentiableOn ℂ h s) (hcont : Continuous h) {δ : ℝ} (hδ : 0 < δ) {z : ℂ}
    (hz : closedBall z δ ⊆ s) : mollify h (moll δ) z = h z := by sorry

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