To Single Accept language eq
Cslib.Automata.εNA.FinAcc.toSingleAccept_language_eq
Plain-language statement
toSingleAccept preserves the language of the input automaton.
Exact Lean statement
@[scoped grind =]
theorem toSingleAccept_language_eq {a : εNA.FinAcc State Symbol} :
language a.toSingleAccept = language aFormal artifact
Lean source
@[scoped grind =]theorem toSingleAccept_language_eq {a : εNA.FinAcc State Symbol} : language a.toSingleAccept = language a := by ext xs apply Iff.intro <;> intro h case mp => rcases h with ⟨os, hos, os', hos', hsmtr⟩ rcases hos with ⟨s, hs₁, hs₂⟩ exists s grind case mpr => rcases h with ⟨s, hs, s', hs', hsmtr⟩ refine ⟨s, by grind, none, by grind, ?_⟩ rw [show xs.map some = xs.map some ++ [] by simp] exact LTS.SMTr.comp (toSingleAccept_sMTr_sMTr.mpr hsmtr) <| LTS.SMTr.τ (LTS.STr.single hs')- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Computability/Automata/EpsilonNA/ToSingleAccept.lean:261-275
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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.