Plain-language statement
The language accepted by c.toDA with a unique accepting state s is exactly the equivalence class of s.
Exact Lean statement
theorem acc_lang_congr [Inhabited A] (s : c.toDA.State) :
c.toDA.toNA.AcceptedLang {s} = c.EqvCls sFormal artifact
Lean source
theorem acc_lang_congr [Inhabited A] (s : c.toDA.State) : c.toDA.toNA.AcceptedLang {s} = c.EqvCls s := by ext al ; simp [Automata.NA.AcceptedLang, Automata.NA.FinAccept] ; constructor · rintro ⟨n, as, ⟨ss, h_run, rfl⟩, rfl⟩ have h_ss_n := Automata.da_fin_run_unique h_run n (by omega) simp [h_ss_n, automaton_congr_run, Congruence.EqvCls] · rintro ⟨rfl⟩ use al.length, al.padDefault ; simp [extract_padDefault] use (c.toDA.DetRun al.padDefault) ; constructor · exact Automata.da_fin_run_exists al.length al.padDefault · simp [automaton_congr_run, extract_padDefault]- Project
- Automata Theory
- License
- Apache-2.0
- Commit
- f196548710ce
- Source
- AutomataTheory/Automata/Congr.lean:51-61
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Related declarations
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.
Acc lang inter
Automata.acc_lang_inter
Plain-language statement
The language accepted by the product NA is the intersection of the languages accepted by the component automata.
Source project: Automata Theory
Person-level attribution pending.