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 LFormal artifact
Lean source
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
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.
Source project: Automata Theory
Person-level attribution pending.
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.
Source project: Automata Theory
Person-level attribution pending.
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.
Source project: Automata Theory
Person-level attribution pending.