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

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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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Project-declaredLean 4.24.0-rc1

Na hist inf run exists

Automata.na_hist_inf_run_exists

Plain-language statement

Any infinite run of the original NA can be extended to an infinite 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.

View proof record