`BookProof.WeylCauchyRiemann.mollify_comm` {F : ℂ → ℂ} (hF : Integrable F) {χ₁ χ₂ : ℂ → ℝ} (hχ₁ : Continuous χ₁) (hχ₁c : HasCompactSupport χ₁) (hχ₂ : Continuous...

Proved

BookProof.WeylCauchyRiemann.mollify_comm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylCauchyRiemann.

BookProof.WeylCauchyRiemann.mollify_comm {F : ℂ → ℂ} (hF : Integrable F) {χ₁ χ₂ : ℂ → ℝ} (hχ₁ : Continuous χ₁) (hχ₁c : HasCompactSupport χ₁) (hχ₂ : Continuous χ₂) (hχ₂c : HasCompactSupport χ₂) : mollify (mollify F χ₁) χ₂ = mollify (mollify F χ₂) χ₁

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

Preamble

-- Generated from ChapterWeylCauchyRiemann.lean — theorem BookProof.WeylCauchyRiemann.mollify_comm
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.mollify_comm {F : ℂ → ℂ} (hF : Integrable F) {χ₁ χ₂ : ℂ → ℝ}
    (hχ₁ : Continuous χ₁) (hχ₁c : HasCompactSupport χ₁)
    (hχ₂ : Continuous χ₂) (hχ₂c : HasCompactSupport χ₂) :
    mollify (mollify F χ₁) χ₂ = mollify (mollify F χ₂) χ₁ := by sorry

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