Na hist inf run exists
Automata.na_hist_inf_run_exists
Plain-language statement
Any infinite run of the original NA can be extended to an infinite run of the history NA, assuming that the history component can always "follow along".
Exact Lean statement
theorem na_hist_inf_run_exists {as : Stream' A} {ss : Stream' M.State}
(h_init : hist_init.Nonempty) (h_next : ∀ s a, (hist_next s a).Nonempty)
(h : M.InfRun as ss) : ∃ hs : Stream' H, (M.addHist hist_init hist_next).InfRun as (fun k ↦ (ss k, hs k))Formal artifact
Lean source
theorem na_hist_inf_run_exists {as : Stream' A} {ss : Stream' M.State} (h_init : hist_init.Nonempty) (h_next : ∀ s a, (hist_next s a).Nonempty) (h : M.InfRun as ss) : ∃ hs : Stream' H, (M.addHist hist_init hist_next).InfRun as (fun k ↦ (ss k, hs k)) := by obtain ⟨hs0, h_hs0⟩ := h_init choose hs' h_hs' using h_next let hs := MakeHist as ss hs0 hs' use hs ; constructor · simp [NA.addHist, MakeHist, h.1, hs] exact h_hs0 · intro k simp [NA.addHist, MakeHist, hs, h.2 k] apply h_hs'- Project
- Automata Theory
- License
- Apache-2.0
- Commit
- f196548710ce
- Source
- AutomataTheory/Automata/Hist.lean:83-94
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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.