Det muller lang union
det_muller_lang_union
Plain-language statement
Deterministic Muller languages are closed under union.
Exact Lean statement
theorem det_muller_lang_union {L0 L1 : Set (Stream' A)}
(h0 : DetMullerLang L0) (h1 : DetMullerLang L1) : DetMullerLang (L0 ∪ L1)Formal artifact
Lean source
theorem det_muller_lang_union {L0 L1 : Set (Stream' A)} (h0 : DetMullerLang L0) (h1 : DetMullerLang L1) : DetMullerLang (L0 ∪ L1) := by obtain ⟨M0, accSet0, h_fin0, rfl⟩ := h0 obtain ⟨M1, accSet1, h_fin1, rfl⟩ := h1 let M : Fin 2 → Automata.DA A | 0 => M0 | 1 => M1 let accSet : (i : Fin 2) → Set (Set (M i).State) | 0 => accSet0 | 1 => accSet1 use (Automata.DA.Prod M), (Automata.DA.MullerAcc_Union M accSet) have : ∀ i, Finite (M i).State := by simp [Fin.forall_fin_two] ; grind constructor · exact Automata.da_prod_finite M · ext as simp [Automata.det_muller_accept_union M accSet as, Fin.exists_fin_two] ; grind- Project
- Automata Theory
- License
- Apache-2.0
- Commit
- f196548710ce
- Source
- AutomataTheory/Languages/DetMullerLang.lean:93-108
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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.