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Project-declaredLean 4.33.0-rc1 · mathlib@169c26b52a38

Is Regular inf

Cslib.ωLanguage.IsRegular.inf

Plain-language statement

The intersection of two ω-regular languages is ω-regular.

Exact Lean statement

@[simp]
theorem IsRegular.inf {p1 p2 : ωLanguage Symbol}
    (h1 : p1.IsRegular) (h2 : p2.IsRegular) : (p1 ⊓ p2).IsRegular

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
@[simp]theorem IsRegular.inf {p1 p2 : ωLanguage Symbol}    (h1 : p1.IsRegular) (h2 : p2.IsRegular) : (p1 ⊓ p2).IsRegular := by  obtain State1, h_fin1, na1, acc1, rfl := h1  obtain State2, h_fin1, na2, acc2, rfl := h2  let State : Bool  Type    | false => State1 | true => State2  let na : (i : Bool)  NA (State i) Symbol    | false => na1 | true => na2  let acc : (i : Bool)  Set (State i)    | false => acc1 | true => acc2  have :  i, Finite (State i) := by grind  use (Π i : Bool, State i) × Bool, inferInstance, (interNA na acc), interAccept acc  apply mem_ext  intro xs  simp only [inter_language_eq, mem_inf, mem_language]  rw [mem_iInf, Bool.forall_bool]  rfl
Project
Lean Computer Science Library
License
Apache-2.0
Commit
f36649cff2c9
Source
Cslib/Computability/Languages/OmegaRegularLanguage.lean:129-146

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Related declarations

Project-declaredLean 4.33.0-rc1

Unique minimal

Cslib.Automata.DA.FinAcc.unique_minimal

Plain-language statement

The minimal DFA M accepting the language l is unique up to unique isomorphism.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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Project-declaredLean 4.33.0-rc1

Buchi Family cover

Cslib.Automata.NA.Buchi.buchiFamily_cover

Project documentation

na.buchiFamily is a cover if na has only finitely many states. This theorem uses the Ramsey theorem for infinite graphs and does not depend on any details of na.BuchiCongruence other than that it is of finite index.

computer sciencecomputabilityprogram semantics

Source project: Lean Computer Science Library

Person-level attribution pending.

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