Is Regular mul
Cslib.Language.IsRegular.mul
Plain-language statement
The concatenation of two regular languages is regular.
Exact Lean statement
@[simp]
theorem IsRegular.mul {l1 l2 : Language Symbol}
(h1 : l1.IsRegular) (h2 : l2.IsRegular) : (l1 * l2).IsRegularFormal artifact
Lean source
@[simp]theorem IsRegular.mul {l1 l2 : Language Symbol} (h1 : l1.IsRegular) (h2 : l2.IsRegular) : (l1 * l2).IsRegular := by obtain (he | hne) := isEmpty_or_nonempty Symbol · obtain (rfl | rfl) := Language.eq_zero_or_one_ofIsEmpty l1 <;> obtain (rfl | rfl) := Language.eq_zero_or_one_ofIsEmpty l2 <;> simp · have := Classical.inhabited_of_nonempty hne rw [IsRegular.iff_nfa] at h1 h2 ⊢ obtain ⟨State1, h_fin1, nfa1, rfl⟩ := h1 obtain ⟨State2, h_fin1, nfa2, rfl⟩ := h2 use Option State1 ⊕ Option State2, inferInstance, ⟨finConcat nfa1 nfa2, inr '' (some '' nfa2.accept)⟩ exact finConcat_language_eq- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Computability/Languages/RegularLanguage.lean:156-168
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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
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Source project: Lean Computer Science Library
Person-level attribution pending.
Buchi Family saturation
Cslib.Automata.NA.Buchi.buchiFamily_saturation
Plain-language statement
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Source project: Lean Computer Science Library
Person-level attribution pending.