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 4.33.0-rc1

Concat language eq

Cslib.Automata.NA.Buchi.concat_language_eq

Plain-language statement

The Buchi automaton formed from concat na1 na2 accepts the ω-language that is the concatenation of the language of na1 and the ω-language of na2.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Inter freq acc freq acc

Cslib.Automata.NA.Buchi.inter_freq_acc_freq_acc

Plain-language statement

If the intersection automaton sees one accepting condition infinitely many times, then it sees the other accepting condition infinitely many times as well.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Inter freq comp acc freq acc

Cslib.Automata.NA.Buchi.inter_freq_comp_acc_freq_acc

Plain-language statement

If the intersection automaton sees the accepting conditions of both component automata infinitely many times, then its own accepting condition also happens infinitely many times.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Inter language eq

Cslib.Automata.NA.Buchi.inter_language_eq

Plain-language statement

The language accepted by the intersection automaton is the intersection of the languages accepted by the two component automata.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Language eq fin i Sup hmul omega Pow

Cslib.Automata.NA.Buchi.language_eq_fin_iSup_hmul_omegaPow

Plain-language statement

The ω-language accepted by a finite-state Büchi automaton is the finite union of ω-languages of the form L * M^ω, where all Ls and Ms are regular languages.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Concat run exists

Cslib.Automata.NA.concat_run_exists

Plain-language statement

Given an accepting finite run of na1 and a run of na2, there exists a run of concat na1 na2 that is the concatenation of the two runs.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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