Import context: Analysis/BakryEmery/IntegrationByParts/WeakHessianEvolution

Definition

KLSModular_FunctionalInequalities_Analysis_BakryEmery_IntegrationByParts_WeakHessianEvolution

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

analysisfunctional-inequalitiesimport-contextklskls-conjecturekls-modularlog-concavemodule-context

This bundle retains the import context of the source module FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.WeakHessianEvolution 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.Lipschitz.Gradient, FunctionalInequalities.Analysis.WeakDerivative.Basic, FunctionalInequalities.Analysis.WeakDerivative.Calculus, FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.InverseHessian.Weak, FunctionalInequalities.Analysis.BakryEmery.MongeAmpere, FunctionalInequalities.Analysis.BakryEmery.Bochner.Basic, and FunctionalInequalities.Analysis.Matrix.Integral.

Original module imports

import FunctionalInequalities.Analysis.Lipschitz.Gradient
import FunctionalInequalities.Analysis.WeakDerivative.Basic
import FunctionalInequalities.Analysis.WeakDerivative.Calculus
import FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.InverseHessian.Weak
import FunctionalInequalities.Analysis.BakryEmery.MongeAmpere
import FunctionalInequalities.Analysis.BakryEmery.Bochner.Basic
import FunctionalInequalities.Analysis.Matrix.Integral

Module navigation

Direct project imports: Analysis/Lipschitz/Gradient, Analysis/WeakDerivative/Basic, Analysis/WeakDerivative/Calculus, Analysis/BakryEmery/IntegrationByParts/InverseHessian/Weak, Analysis/BakryEmery/MongeAmpere, Analysis/BakryEmery/Bochner/Basic, Analysis/Matrix/Integral.

Theorems in source order:

Project result: The KLS conjecture.

Original module · FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.WeakHessianEvolution · Frozen source 408915f.

Definition code

import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Lipschitz_Gradient
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_WeakDerivative_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_WeakDerivative_Calculus
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_IntegrationByParts_InverseHessian_Weak
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_MongeAmpere
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_Bochner_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_Integral

Source

Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/Analysis/BakryEmery/IntegrationByParts/WeakHessianEvolution.lean#L1-L2100 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.WeakHessianEvolution`, import-context bundle `KLSModular_FunctionalInequalities_Analysis_BakryEmery_IntegrationByParts_WeakHessianEvolution`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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