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

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Project-declaredLean 4.33.0-rc1

Frequently in finite type

Cslib.ωSequence.frequently_in_finite_type

Plain-language statement

In a finite type, the elements of a set occurs infinitely often iff some element in the set occurs infinitely often.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Frequently in strict Mono

Cslib.ωSequence.frequently_in_strictMono

Plain-language statement

If p is true infinitely often, then p is true in infinitely many segments of any strictly monotonic function f.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Frequently in finite set

frequently_in_finite_set

Plain-language statement

Note that only the → direction needs the finiteness assumption.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Inf occ eventually

inf_occ_eventually

Plain-language statement

Over a finite type, xs k is in InfOcc xs for all sufficiently large k.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Inf occ pair

inf_occ_pair

Plain-language statement

Same as inf_acc_proj, but for pair types. This result does follow from inf_occ_proj, but that proof (see below) turns out to be longer.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Inf occ proj

inf_occ_proj

Plain-language statement

Note that only the ⊇ direction needs the finiteness assumptions.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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