`BookProof.WeylCauchyRiemann.dbar_eq_zero_of_notMem_tsupport` {φ : ℂ → ℂ} {z : ℂ} (hz : z ∉ tsupport φ) : dbar φ z = 0

Proved

BookProof.WeylCauchyRiemann.dbar_eq_zero_of_notMem_tsupport

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylCauchyRiemann.

BookProof.WeylCauchyRiemann.dbar_eq_zero_of_notMem_tsupport {φ : ℂ → ℂ} {z : ℂ} (hz : z ∉ tsupport φ) : dbar φ z = 0

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

Preamble

-- Generated from ChapterWeylCauchyRiemann.lean — theorem BookProof.WeylCauchyRiemann.dbar_eq_zero_of_notMem_tsupport
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.dbar_eq_zero_of_notMem_tsupport {φ : ℂ → ℂ} {z : ℂ} (hz : z ∉ tsupport φ) :
    dbar φ z = 0 := by sorry

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