`BookProof.HalfLineLimitCircle.hlKin_coeFn` (f : testSpace) : ((hlKin (hlEquiv f) : HL) : ℝ → ℂ) =ᵐ[hlMeasure] fun x => -deriv (deriv (f : ℝ → ℂ)) x

Proved

BookProof.HalfLineLimitCircle.hlKin_coeFn

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHalfLineLimitCircle.

BookProof.HalfLineLimitCircle.hlKin_coeFn (f : testSpace) : ((hlKin (hlEquiv f) : HL) : ℝ → ℂ) =ᵐ[hlMeasure] fun x => -deriv (deriv (f : ℝ → ℂ)) x

Formalization note: Lean 4 identifier BookProof.HalfLineLimitCircle.hlKin_coeFn.

Preamble

-- Generated from ChapterHalfLineLimitCircle.lean — theorem BookProof.HalfLineLimitCircle.hlKin_coeFn
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterHalfLineLimitCircle
open BookProof.HalfLineLimitCircle



open MeasureTheory Set BookProof.FarisLavine

noncomputable section

local notation "smoothTop" => ((⊤ : ℕ∞) : WithTop ℕ∞)

Formal statement

theorem BookProof.HalfLineLimitCircle.hlKin_coeFn (f : testSpace) :
    ((hlKin (hlEquiv f) : HL) : ℝ → ℂ) =ᵐ[hlMeasure] fun x => -deriv (deriv (f : ℝ → ℂ)) x := by sorry

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