Import context: KLS/CEK/MomentRegularity/WeakDerivative

Definition

KLSModular_FunctionalInequalities_KLS_CEK_MomentRegularity_WeakDerivative

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

functional-inequalitiesimport-contextklskls-conjecturekls-modularlog-concavemodule-context

This bundle retains the import context of the source module FunctionalInequalities.KLS.CEK.MomentRegularity.WeakDerivative 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.Analysis.BakryEmery.HessianOperator, FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.InverseHessian.Weak, FunctionalInequalities.Analysis.BakryEmery.WeakHessian, FunctionalInequalities.Analysis.Convex.Coercivity, FunctionalInequalities.Analysis.Convex.GradientLipschitz, FunctionalInequalities.Analysis.Convex.HessianRegularity, FunctionalInequalities.Analysis.Lipschitz.Exponential, FunctionalInequalities.Analysis.Lipschitz.Gradient, FunctionalInequalities.Analysis.Matrix.DeterminantDerivative, FunctionalInequalities.Analysis.Matrix.WeakDerivative, FunctionalInequalities.Analysis.WeakDerivative.Basic, FunctionalInequalities.KLS.Isotropic, and FunctionalInequalities.KLS.CEK.MomentRegularity.Potential.

Original module imports

import FunctionalInequalities.Analysis.BakryEmery.HessianOperator
import FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.InverseHessian.Weak
import FunctionalInequalities.Analysis.BakryEmery.WeakHessian
import FunctionalInequalities.Analysis.Convex.Coercivity
import FunctionalInequalities.Analysis.Convex.GradientLipschitz
import FunctionalInequalities.Analysis.Convex.HessianRegularity
import FunctionalInequalities.Analysis.Lipschitz.Exponential
import FunctionalInequalities.Analysis.Lipschitz.Gradient
import FunctionalInequalities.Analysis.Matrix.DeterminantDerivative
import FunctionalInequalities.Analysis.Matrix.WeakDerivative
import FunctionalInequalities.Analysis.WeakDerivative.Basic
import FunctionalInequalities.KLS.Isotropic
import FunctionalInequalities.KLS.CEK.MomentRegularity.Potential

Module navigation

Direct project imports: Analysis/BakryEmery/HessianOperator, Analysis/BakryEmery/IntegrationByParts/InverseHessian/Weak, Analysis/BakryEmery/WeakHessian, Analysis/Convex/Coercivity, Analysis/Convex/GradientLipschitz, Analysis/Convex/HessianRegularity, Analysis/Lipschitz/Exponential, Analysis/Lipschitz/Gradient, Analysis/Matrix/DeterminantDerivative, Analysis/Matrix/WeakDerivative, Analysis/WeakDerivative/Basic, KLS/Isotropic, KLS/CEK/MomentRegularity/Potential.

Theorems in source order:

Project result: The KLS conjecture.

Original module · FunctionalInequalities.KLS.CEK.MomentRegularity.WeakDerivative · Frozen source 408915f.

Definition code

import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_HessianOperator
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_IntegrationByParts_InverseHessian_Weak
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_WeakHessian
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_Coercivity
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_GradientLipschitz
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_HessianRegularity
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Lipschitz_Exponential
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Lipschitz_Gradient
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_DeterminantDerivative
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_WeakDerivative
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_WeakDerivative_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_Isotropic
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_CEK_MomentRegularity_Potential

Source

Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/KLS/CEK/MomentRegularity/WeakDerivative.lean#L1-L291 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.KLS.CEK.MomentRegularity.WeakDerivative`, import-context bundle `KLSModular_FunctionalInequalities_KLS_CEK_MomentRegularity_WeakDerivative`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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