Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 136 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.33.0-rc1

Context complete

Cslib.CCS.Context.complete

Plain-language statement

Any Process can be obtained by filling a Context with an atom. This proves that Context is a complete formalisation of syntactic contexts for CCS.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

M Yields m Tr

Cslib.Computability.Turing.SingleTape.SingleTapeNTM.mYields_mTr

Plain-language statement

Characterisation of executions in terms of multistep transitions.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Perfectly Secret iff indep

Cslib.Crypto.Protocols.PerfectSecrecy.perfectlySecret_iff_indep

Plain-language statement

Perfect secrecy is equivalent to message-ciphertext independence. The two formulations are related by multiplying/dividing by marginal(c).

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Shannon Key Space

Cslib.Crypto.Protocols.PerfectSecrecy.shannonKeySpace

Project documentation

Perfect secrecy requires |K| ≥ |M| (Shannon's theorem).

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Nat Degree sharing Polynomial le

Cslib.Crypto.Protocols.SecretSharing.Shamir.Polynomial.natDegree_sharingPolynomial_le

Plain-language statement

If the tail polynomial has degree < n, then the sharing polynomial has natural degree at most n.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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