`BookProof.WeylCauchyRiemann.WeakCauchyRiemannOn.congr_ae` {f g : ℂ → ℂ} {U : Set ℂ} (hg : WeakCauchyRiemannOn g U) (hae : ∀ᵐ z : ℂ, z ∈ U → f z = g z) : WeakCauchyRiemannOn f U

Proved

BookProof.WeylCauchyRiemann.WeakCauchyRiemannOn.congr_ae

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylCauchyRiemann.

BookProof.WeylCauchyRiemann.WeakCauchyRiemannOn.congr_ae {f g : ℂ → ℂ} {U : Set ℂ} (hg : WeakCauchyRiemannOn g U) (hae : ∀ᵐ z : ℂ, z ∈ U → f z = g z) : WeakCauchyRiemannOn f U

Formalization note: Lean 4 identifier BookProof.WeylCauchyRiemann.WeakCauchyRiemannOn.congr_ae.

Preamble

-- Generated from ChapterWeylCauchyRiemann.lean — theorem BookProof.WeylCauchyRiemann.WeakCauchyRiemannOn.congr_ae
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.WeakCauchyRiemannOn.congr_ae {f g : ℂ → ℂ} {U : Set ℂ}
    (hg : WeakCauchyRiemannOn g U) (hae : ∀ᵐ z : ℂ, z ∈ U → f z = g z) :
    WeakCauchyRiemannOn f U := by sorry

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