Import context: Poincare/LocalSlope/SmoothTestComparison

Definition

KLSModular_FunctionalInequalities_Poincare_LocalSlope_SmoothTestComparison

by Lazyfill · Oct 25, 2026 · Mathlib 0df444a (Lean v4.33.1)

functional-inequalitiesimport-contextklskls-conjecturekls-modularlog-concavemodule-contextpoincare-inequality

This bundle retains the import context of the source module FunctionalInequalities.Poincare.LocalSlope.SmoothTestComparison in the modular KLS dependency graph. It adds no new mathematical declarations. Substantive statements and proofs are represented by separate theorem nodes.

Its direct project prerequisite modules are FunctionalInequalities.Energy.Euclidean.LipschitzApproximation.Approximation, FunctionalInequalities.Poincare.LocalSlope.Basic, FunctionalInequalities.Energy.LocalSlope.Gradient, and FunctionalInequalities.Poincare.SmoothTest.Comparison. It also directly imports the external prerequisite modules Mathlib.Analysis.Calculus.ContDiff.RCLike and Mathlib.MeasureTheory.Function.LpSpace.Complete.

Original module imports

import FunctionalInequalities.Energy.Euclidean.LipschitzApproximation.Approximation
import FunctionalInequalities.Poincare.LocalSlope.Basic
import FunctionalInequalities.Energy.LocalSlope.Gradient
import FunctionalInequalities.Poincare.SmoothTest.Comparison
import Mathlib.Analysis.Calculus.ContDiff.RCLike
import Mathlib.MeasureTheory.Function.LpSpace.Complete

Module navigation

Direct project imports: Energy/Euclidean/LipschitzApproximation/Approximation, Poincare/LocalSlope/Basic, Energy/LocalSlope/Gradient, Poincare/SmoothTest/Comparison.

Theorems in source order:

holds_iff_localSlope

Project result: The KLS conjecture.

Original module · FunctionalInequalities.Poincare.LocalSlope.SmoothTestComparison · Frozen source 408915f.

Definition code

import Definitions.Def_KLSModular_FunctionalInequalities_Energy_Euclidean_LipschitzApproximation_Approximation
import Definitions.Def_KLSModular_FunctionalInequalities_Poincare_LocalSlope_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Energy_LocalSlope_Gradient
import Definitions.Def_KLSModular_FunctionalInequalities_Poincare_SmoothTest_Comparison
import Mathlib.Analysis.Calculus.ContDiff.RCLike
import Mathlib.MeasureTheory.Function.LpSpace.Complete

Source

Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/Poincare/LocalSlope/SmoothTestComparison.lean#L1-L217 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.Poincare.LocalSlope.SmoothTestComparison`, import-context bundle `KLSModular_FunctionalInequalities_Poincare_LocalSlope_SmoothTestComparison`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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