`BookProof.WeylCauchyRiemann.deriv_slice_re` {ψ : ℂ → ℂ} (hψ : Differentiable ℝ ψ) (x y : ℝ) : deriv (fun t : ℝ => ψ ((t : ℂ) + y * Complex.I)) x = fderiv ℝ ψ ((x : ℂ) + y...

Proved

BookProof.WeylCauchyRiemann.deriv_slice_re

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylCauchyRiemann.

BookProof.WeylCauchyRiemann.deriv_slice_re {ψ : ℂ → ℂ} (hψ : Differentiable ℝ ψ) (x y : ℝ) : deriv (fun t : ℝ => ψ ((t : ℂ) + y * Complex.I)) x = fderiv ℝ ψ ((x : ℂ) + y * Complex.I) 1

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

Preamble

-- Generated from ChapterWeylCauchyRiemann.lean — theorem BookProof.WeylCauchyRiemann.deriv_slice_re
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.deriv_slice_re {ψ : ℂ → ℂ} (hψ : Differentiable ℝ ψ) (x y : ℝ) :
    deriv (fun t : ℝ => ψ ((t : ℂ) + y * Complex.I)) x
      = fderiv ℝ ψ ((x : ℂ) + y * Complex.I) 1 := by sorry

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