Plain-language statement
The language accepted by M.Pset is the same as that accepted by M, where the accepting states of M.Pset are those that contains at least one accepting state of M.
Exact Lean statement
theorem acc_lang_pset :
M.PSet.toNA.AcceptedLang (M.PSet_Acc acc) = M.AcceptedLang accFormal artifact
Lean source
theorem acc_lang_pset : M.PSet.toNA.AcceptedLang (M.PSet_Acc acc) = M.AcceptedLang acc := by ext al ; simp only [NA.AcceptedLang, NA.FinAccept] ; constructor · rintro ⟨n, as, ⟨ss', h_run', h_acc'⟩, h_al⟩ have h_sn' := da_fin_run_unique h_run' n (by omega) rw [na_pset_run] at h_sn' simp [h_sn', NA.PSet_Acc] at h_acc' obtain ⟨sn, ⟨ss, h_run, h_sn⟩, h_acc⟩ := h_acc' use n, as ; simp [h_al] use ss ; simp [h_run, h_sn, h_acc] · rintro ⟨n, as, ⟨ss, h_run, h_sn⟩, h_al⟩ use n, as ; simp [h_al] use (M.PSet.DetRun as) ; constructor · apply da_fin_run_exists · rw [na_pset_run, NA.PSet_Acc] use (ss n) ; simp [h_sn] ; use ss- Project
- Automata Theory
- License
- Apache-2.0
- Commit
- f196548710ce
- Source
- AutomataTheory/Automata/PSet.lean:88-103
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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.