`BookProof.WeylCauchyRiemann.hasCompactSupport_comp_realProd` {F : ℂ → ℂ} (hF : HasCompactSupport F) : HasCompactSupport (fun p : ℝ × ℝ => F ((p.1 : ℂ) + p.2 * Complex.I))

Proved

BookProof.WeylCauchyRiemann.hasCompactSupport_comp_realProd

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylCauchyRiemann.

BookProof.WeylCauchyRiemann.hasCompactSupport_comp_realProd {F : ℂ → ℂ} (hF : HasCompactSupport F) : HasCompactSupport (fun p : ℝ × ℝ => F ((p.1 : ℂ) + p.2 * Complex.I))

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

Preamble

-- Generated from ChapterWeylCauchyRiemann.lean — theorem BookProof.WeylCauchyRiemann.hasCompactSupport_comp_realProd
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.hasCompactSupport_comp_realProd {F : ℂ → ℂ} (hF : HasCompactSupport F) :
    HasCompactSupport (fun p : ℝ × ℝ => F ((p.1 : ℂ) + p.2 * Complex.I)) := by sorry

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