trureturingGitHub MATHEMATICAL ATLAS

Entropy / CONCEPT

Mutual-Information Chain Rule

For a finite joint law, the information in a pair of observations splits into the information in the first observation and the remaining conditional information.

Closed Authored exposition
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES4
PROOF DEPTH7
DOCUMENT LINKS1
THEOREM

Mutual information obeys the chain rule

RELATIONSHIP ATLAS

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Direct recorded relationships
Symmetry of Finite Mutual InformationSymmetry of Finite MutualInformationMarkov Data ProcessingMarkov Data ProcessingMutual-Information Chain RuleMutual-Information Chain RuleConditional Information PostprocessingConditional InformationPostprocessingCanonical Conditional Information SubmodularityCanonical ConditionalInformation SubmodularityConditional-Independent Information SubmodularityConditional-IndependentInformation SubmodularityPredictive Memory under Deterministic RefinementPredictive Memory underDeterministic Refinement
Proof dependencyStructural affinityDocument link

RELATED KNOWLEDGE

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Documents & exposition

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LIBRARY / RELEASE VERSIONS

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Certified provenance

Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
7
Layer
D5/S3
Domain
Entropy
Node ID
D5/S3/Entropy/Submodularity/MutualInformationChainRule
Repository path
D5/S3/Entropy/Submodularity/MutualInformationChainRule.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

Authority boundary

Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.