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Project-declaredLean 4.24.0-rc1 · mathlib@aad26963

Omega reg lang imp det muller lang

omega_reg_lang_imp_det_muller_lang

Plain-language statement

Every deterministic Muller language is an ω-regular language.

Exact Lean statement

theorem omega_reg_lang_imp_det_muller_lang [Inhabited A] {L : Set (Stream' A)}
    (h : OmegaRegLang L) : DetMullerLang L

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
theorem omega_reg_lang_imp_det_muller_lang [Inhabited A] {L : Set (Stream' A)}    (h : OmegaRegLang L) : DetMullerLang L := by  obtain n, U, V, h_reg, rfl := omega_reg_lang_iff_finite_union_form.mp h  rw [ biUnion_univ] ; apply det_muller_lang_biUnion  intro i _ ; apply det_muller_lang_concat  · exact (h_reg i).1  · have h_v := (h_reg i).2    obtain W, h_w, h_omega := choueka_lemma h_v    rw [h_omega] ; apply det_muller_lang_concat    · exact reg_lang_iter h_v    · exact det_muller_lang_omega_limit h_w
Project
Automata Theory
License
Apache-2.0
Commit
f196548710ce
Source
AutomataTheory/Languages/DetMullerLang.lean:175-185

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Related declarations

Project-declaredLean 4.24.0-rc1

Acc lang congr

acc_lang_congr

Plain-language statement

The language accepted by c.toDA with a unique accepting state s is exactly the equivalence class of s.

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Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Acc lang concat e

Automata.acc_lang_concat_e

Plain-language statement

The language of the concatenation NA that is accepted by M0's accepting states is the language accepted by M0.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Acc lang concat ne

Automata.acc_lang_concat_ne

Plain-language statement

The language of the concatenation NA that is accepted by M1's accepting states is the language accepted by M0 concatenated with the language accepted by M1 minus the empty word.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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