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

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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Project-declaredLean 4.33.0-rc1

Concat run proj

Cslib.Automata.NA.concat_run_proj

Plain-language statement

A run of concat na1 na2 containing at least one na2 state is the concatenation of an accepting finite run of na1 followed by a run 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

Fin Concat language eq

Cslib.Automata.NA.FinAcc.finConcat_language_eq

Plain-language statement

finConcat na1 na2 accepts the concatenation of the languages of na1 and na2.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Loop language eq

Cslib.Automata.NA.FinAcc.loop_language_eq

Plain-language statement

finLoop na accepts the Kleene star of the language of na, assuming that the latter is nonempty.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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