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 199 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.24.0-rc1

Pair acc lang regular

Automata.pair_acc_lang_regular

Plain-language statement

If M is finite-state, then M.PairAccLang acc s s' is regular for any pair of states s and s'. Note that we need to use the history NA construction to prove this result, because the NA needs to remember whether an accepting state has been visited.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Pair lang regular

Automata.pair_lang_regular

Plain-language statement

If M is finite-state, then M.PairLang s s' is regular for any pair of states s and s'.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Ramsey lemma

Automata.ramsey_lemma

Project documentation

This lemma derives a form of the Ramsey theorem suitable for use in the next theorem.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Unique minimal

Cslib.Automata.DA.FinAcc.unique_minimal

Plain-language statement

The minimal DFA M accepting the language l is unique up to unique isomorphism.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Buchi Family cover

Cslib.Automata.NA.Buchi.buchiFamily_cover

Project documentation

na.buchiFamily is a cover if na has only finitely many states. This theorem uses the Ramsey theorem for infinite graphs and does not depend on any details of na.BuchiCongruence other than that it is of finite index.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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