Prove2Me

Import context: Analysis/Convex/SecondOrder

Definition
KLSModular_FunctionalInequalities_Analysis_Convex_SecondOrder

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.Convex.SecondOrder 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.Convex.Subgradient, FunctionalInequalities.Analysis.Convex.Proximal, and FunctionalInequalities.Analysis.Sard.Equidimensional. It also directly imports the external prerequisite modules Mathlib.MeasureTheory.Integral.Lebesgue.Add, Mathlib.Analysis.Calculus.Taylor, Mathlib.Analysis.Calculus.ContDiff.Convolution, Mathlib.Analysis.Calculus.Rademacher, and Mathlib.MeasureTheory.Function.Jacobian.

Original module imports

import FunctionalInequalities.Analysis.Convex.Subgradient
import FunctionalInequalities.Analysis.Convex.Proximal
import Mathlib.MeasureTheory.Integral.Lebesgue.Add
import Mathlib.Analysis.Calculus.Taylor
import Mathlib.Analysis.Calculus.ContDiff.Convolution
import FunctionalInequalities.Analysis.Sard.Equidimensional
import Mathlib.Analysis.Calculus.Rademacher
import Mathlib.MeasureTheory.Function.Jacobian

Module navigation

Direct project imports: Analysis/Convex/Subgradient, Analysis/Convex/Proximal, Analysis/Sard/Equidimensional.

Theorems in source order:

Project result: The KLS conjecture.

Original module · FunctionalInequalities.Analysis.Convex.SecondOrder · Frozen source 408915f.

Definition code
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_Subgradient
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_Proximal
import Mathlib.MeasureTheory.Integral.Lebesgue.Add
import Mathlib.Analysis.Calculus.Taylor
import Mathlib.Analysis.Calculus.ContDiff.Convolution
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Sard_Equidimensional
import Mathlib.Analysis.Calculus.Rademacher
import Mathlib.MeasureTheory.Function.Jacobian
Source
Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/Analysis/Convex/SecondOrder.lean#L1-L682 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.Analysis.Convex.SecondOrder`, import-context bundle `KLSModular_FunctionalInequalities_Analysis_Convex_SecondOrder`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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