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 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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Project-declaredLean 4.33.0-rc1

I Prod run iff

Cslib.Automata.NA.iProd_run_iff

Plain-language statement

Every run of the product automaton projects onto runs of its component automata, and vice versa.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

I Sum run iff

Cslib.Automata.NA.iSum_run_iff

Plain-language statement

An infinite run of the sum automaton is an infinite run of one of its 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

Loop run exists

Cslib.Automata.NA.loop_run_exists

Plain-language statement

For any infinite sequence xls of nonempty finite words from language na, there is an infinite run of na.loop corresponding to xls.flatten in which the state () marks the boundaries between the finite words in xls.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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