`BookProof.WeylCauchyRiemann.analyticOn_of_dbar_eq_zero` {g : ℂ → ℂ} {s : Set ℂ} (hs : IsOpen s) (hg : ∀ z ∈ s, DifferentiableAt ℝ g z) (hdbar : ∀ z ∈ s, dbar g z = 0) : AnalyticOn

Proved

BookProof.WeylCauchyRiemann.analyticOn_of_dbar_eq_zero

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylCauchyRiemann.

BookProof.WeylCauchyRiemann.analyticOn_of_dbar_eq_zero {g : ℂ → ℂ} {s : Set ℂ} (hs : IsOpen s) (hg : ∀ z ∈ s, DifferentiableAt ℝ g z) (hdbar : ∀ z ∈ s, dbar g z = 0) : AnalyticOn ℂ g s

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

Preamble

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



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

noncomputable section

Formal statement

theorem BookProof.WeylCauchyRiemann.analyticOn_of_dbar_eq_zero {g : ℂ → ℂ} {s : Set ℂ} (hs : IsOpen s)
    (hg : ∀ z ∈ s, DifferentiableAt ℝ g z) (hdbar : ∀ z ∈ s, dbar g z = 0) :
    AnalyticOn ℂ g s := by sorry

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