`BookProof.LimitCircleExample.hasDerivAt_lcLogFun` (x : ℝ) : HasDerivAt (fun y : ℝ => ((lcP y : ℝ) : ℂ) + Complex.I * ((lcQ y : ℝ) : ℂ)) (lcLog' x) x

Proved

BookProof.LimitCircleExample.hasDerivAt_lcLogFun

by leonardopedro · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLimitCircleExample.

BookProof.LimitCircleExample.hasDerivAt_lcLogFun (x : ℝ) : HasDerivAt (fun y : ℝ => ((lcP y : ℝ) : ℂ) + Complex.I * ((lcQ y : ℝ) : ℂ)) (lcLog' x) x

Formalization note: Lean 4 identifier BookProof.LimitCircleExample.hasDerivAt_lcLogFun.

Preamble

-- Generated from ChapterLimitCircleExample.lean — theorem BookProof.LimitCircleExample.hasDerivAt_lcLogFun
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterScalaronCoreEsa
import Definitions.Def_ChapterScalaronWallEsa
import Definitions.Def_ChapterWallDeficiencyObstruction
import Mathlib
import Definitions.Def_ChapterLimitCircleExample
open BookProof.LimitCircleExample



open MeasureTheory Real
open BookProof.FarisLavine BookProof.ScalaronEsa BookProof.ScalaronWallEsa
open BookProof.WallDeficiencyObstruction

noncomputable section

Formal statement

theorem BookProof.LimitCircleExample.hasDerivAt_lcLogFun (x : ℝ) :
    HasDerivAt (fun y : ℝ => ((lcP y : ℝ) : ℂ) + Complex.I * ((lcQ y : ℝ) : ℂ))
      (lcLog' x) x := by sorry

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