Import context: Analysis/Convex/SecondDifference
DefinitionKLSModular_FunctionalInequalities_Analysis_Convex_SecondDifferenceanalysisfunctional-inequalitiesimport-contextklskls-conjecturekls-modularlog-concavemodule-context
This bundle retains the import context of the source module FunctionalInequalities.Analysis.Convex.SecondDifference 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 module is FunctionalInequalities.Analysis.Convex.Subgradient. It also directly imports the external prerequisite module Mathlib.
Original module imports
import Mathlib
import FunctionalInequalities.Analysis.Convex.Subgradient
Module navigation
Direct project imports: Analysis/Convex/Subgradient.
Theorems in source order:
lipschitzWith_gradient_of_second_difference_lesd_penalized_estimatesecondDifference_le_of_penalized_maximacenteredDifference_contDiff_lipschitz_gradientcenteredDifference_nonneg_le
Project result: The KLS conjecture.
Original module · FunctionalInequalities.Analysis.Convex.SecondDifference · Frozen source 408915f.
Definition code
import Mathlib import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_Subgradient
Source
Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/Analysis/Convex/SecondDifference.lean#L1-L875 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.Analysis.Convex.SecondDifference`, import-context bundle `KLSModular_FunctionalInequalities_Analysis_Convex_SecondDifference`). The line range identifies the complete original source module; this bundle preserves only its direct import context.