Plain-language statement
Regular languages are closed under intersection.
Exact Lean statement
theorem reg_lang_inter [Inhabited A] {L0 L1 : Set (List A)}
(h0 : RegLang L0) (h1 : RegLang L1) : RegLang (L0 ∩ L1)Formal artifact
Lean source
theorem reg_lang_inter [Inhabited A] {L0 L1 : Set (List A)} (h0 : RegLang L0) (h1 : RegLang L1) : RegLang (L0 ∩ L1) := by obtain ⟨M0, acc0, h_fin0, h_l0⟩ := h0 obtain ⟨M1, acc1, h_fin1, h_l1⟩ := h1 let M_u : (i : Fin 2) → Automata.NA A | 0 => M0 | 1 => M1 let acc_u : (i : Fin 2) → Set (M_u i).State | 0 => acc0 | 1 => acc1 use (Automata.NA.Prod M_u), (Automata.NA.Prod_Acc M_u acc_u) constructor · have h_fin : ∀ i, Finite (M_u i).State := by simp [Fin.forall_fin_two, M_u, h_fin0, h_fin1] exact Pi.finite · ext as simp [h_l0, h_l1, Automata.acc_lang_inter M_u acc_u, Fin.forall_fin_two, M_u, acc_u]- Project
- Automata Theory
- License
- Apache-2.0
- Commit
- f196548710ce
- Source
- AutomataTheory/Languages/RegLang.lean:102-117
Reuse this declaration
Bring the exact result into your workflow
The import identifies the source module. Your project still needs the pinned package dependency shown on this page.
What this badge means
This completion status comes from the project or community source. It has not yet been represented here as an independent rebuild and axiom audit.
Continue in this project
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.