Det muller lang imp omega reg lang
det_muller_lang_imp_omega_reg_lang
Plain-language statement
Every deterministic Muller language is an ω-regular language.
Exact Lean statement
theorem det_muller_lang_imp_omega_reg_lang [Inhabited A] {L : Set (Stream' A)}
(h : DetMullerLang L) : OmegaRegLang LFormal artifact
Lean source
theorem det_muller_lang_imp_omega_reg_lang [Inhabited A] {L : Set (Stream' A)} (h : DetMullerLang L) : OmegaRegLang L := by obtain ⟨M, accSet, h_fin, rfl⟩ := h rw [Automata.det_muller_accept_boolean_form] have h_reg : ∀ s, RegLang (M.toNA.AcceptedLang {s}) := by intro s ; use M.toNA, {s} ; simp [Automata.DA.toNA, h_fin] apply omega_reg_lang_biUnion ; intro acc h_acc apply omega_reg_lang_inter <;> apply omega_reg_lang_biInter <;> intro s h_s · apply omega_reg_lang_omega_limit simp [h_reg] · apply omega_reg_lang_compl ; apply omega_reg_lang_omega_limit simp [h_reg]- Project
- Automata Theory
- License
- Apache-2.0
- Commit
- f196548710ce
- Source
- AutomataTheory/Languages/DetMullerLang.lean:160-171
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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.