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 2,569 research declarations. Search 10,000 more complete Mathlib declarations.

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2569 results

Project-declaredLean 4.24.0-rc1

Greater subseq lemma

Automata.greater_subseq_lemma

Project documentation

A technical lemma for use in the next theorem.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Na Accepted Lang of Fin Accept

Automata.na_AcceptedLang_of_FinAccept'

Project documentation

The following theorem shows that under the assumption that the alphabet type A is inhabited, the definitions using infinite sequences and those using finite sequences actually define the same notion of the accepted language of an automaton.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Na concat fin run 0

Automata.na_concat_fin_run_0

Plain-language statement

A finite run of the concatenation NA that ends in a state of M0 is completely a run of M0.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Na concat fin run 1

Automata.na_concat_fin_run_1

Plain-language statement

A finite run of the concatenation NA that ends in a state of M1 consists of a run of M0 followed by a run of M1.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Na concat inf run

Automata.na_concat_inf_run

Plain-language statement

An infinite run of the concatenation NA that contains a state of M1 consists of a finite run of M0 followed by an infinite run of M1.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Na hist fin run exists

Automata.na_hist_fin_run_exists

Plain-language statement

Any finite run of the original NA can be extended to a finite run of the history NA, assuming that the history component can always "follow along".

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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