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

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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Project-declaredLean 4.33.0-rc1

Loop run one iter

Cslib.Automata.NA.loop_run_one_iter

Plain-language statement

A run of na.loop containing at least one non-initial () state is the concatenation of a nonempty finite run of na followed by a run of na.loop.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Totalize run mtr

Cslib.Automata.NA.totalize_run_mtr

Plain-language statement

In an infinite execution of NA.totalize, as long as the NA stays in a non-sink state, the execution so far corresponds to a finite execution of the original NA.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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