To NAFin Acc language eq
Cslib.Automata.εNA.FinAcc.toNAFinAcc_language_eq
Plain-language statement
Correctness of toNAFinAcc.
Exact Lean statement
@[scoped grind =]
theorem toNAFinAcc_language_eq {a : εNA.FinAcc State Symbol} :
language a.toNAFinAcc = language aFormal artifact
Lean source
@[scoped grind =]theorem toNAFinAcc_language_eq {a : εNA.FinAcc State Symbol} : language a.toNAFinAcc = language a := by ext xs constructor <;> intro ⟨s, hs, s', hs', h⟩ · have ⟨sStart, h_sStart, hs⟩ : ∃ i ∈ a.start, s ∈ a.saturate.image i HasTau.τ := by simpa [toNAFinAcc, LTS.τClosure, LTS.setImage] using hs use sStart, h_sStart, s', hs' have h_start := (LTS.sTr_τSTr_iff a.toLTS).mp hs exact LTS.SMTr.comp (LTS.sMTr_τSTr_iff.mp h_start) (by grind) · cases xs with | nil => cases h with | τ tau => exact ⟨s', LTS.tr_setImage hs tau, by grind⟩ | cons x xs => exact ⟨s, by grind [Set.mem_of_mem_of_subset]⟩- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Computability/Automata/EpsilonNA/ToNA.lean:30-42
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Related declarations
Unique minimal
Cslib.Automata.DA.FinAcc.unique_minimal
Plain-language statement
The minimal DFA M accepting the language l is unique up to unique isomorphism.
Source project: Lean Computer Science Library
Person-level attribution pending.
Buchi Family cover
Cslib.Automata.NA.Buchi.buchiFamily_cover
Project documentation
na.buchiFamily is a cover if na has only finitely many states. This theorem uses the Ramsey theorem for infinite graphs and does not depend on any details of na.BuchiCongruence other than that it is of finite index.
Source project: Lean Computer Science Library
Person-level attribution pending.
Buchi Family saturation
Cslib.Automata.NA.Buchi.buchiFamily_saturation
Plain-language statement
na.buchiFamily saturates the ω-language accepted by na.
Source project: Lean Computer Science Library
Person-level attribution pending.