Prove2Me

Import context: Probability/Stein/SourceDualBound

Definition
KLSModular_FunctionalInequalities_Probability_Stein_SourceDualBound

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

functional-inequalitiesimport-contextklskls-conjecturekls-modularlog-concavemodule-contextprobability

This bundle retains the import context of the source module FunctionalInequalities.Probability.Stein.SourceDualBound 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.L2.Pairing and FunctionalInequalities.Analysis.BakryEmery.Calculus. It also directly imports the external prerequisite modules Mathlib.MeasureTheory.Measure.ProbabilityMeasure and Mathlib.Analysis.Normed.Lp.MeasurableSpace.

Original module imports

import Mathlib.MeasureTheory.Measure.ProbabilityMeasure
import Mathlib.Analysis.Normed.Lp.MeasurableSpace
import FunctionalInequalities.L2.Pairing
import FunctionalInequalities.Analysis.BakryEmery.Calculus

Module navigation

Direct project imports: L2/Pairing, Analysis/BakryEmery/Calculus.

Theorems in source order:

Project result: The KLS conjecture.

Original module · FunctionalInequalities.Probability.Stein.SourceDualBound · Frozen source 408915f.

Definition code
import Mathlib.MeasureTheory.Measure.ProbabilityMeasure
import Mathlib.Analysis.Normed.Lp.MeasurableSpace
import Definitions.Def_KLSModular_FunctionalInequalities_L2_Pairing
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_Calculus
Source
Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/Probability/Stein/SourceDualBound.lean#L1-L67 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.Probability.Stein.SourceDualBound`, import-context bundle `KLSModular_FunctionalInequalities_Probability_Stein_SourceDualBound`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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