Plain-language statement
Note that only the ⊇ direction needs the finiteness assumptions.
Exact Lean statement
theorem inf_occ_proj {I : Type*} [Finite I] {X : I → Type*} [h : ∀ i, Finite (X i)] (xs : Stream' (Π i, X i)) (i : I) :
(· i) '' (InfOcc xs) = InfOcc ((· i) ∘ xs)Formal artifact
Lean source
theorem inf_occ_proj {I : Type*} [Finite I] {X : I → Type*} [h : ∀ i, Finite (X i)] (xs : Stream' (Π i, X i)) (i : I) : (· i) '' (InfOcc xs) = InfOcc ((· i) ∘ xs) := by ext x_i ; simp ; constructor · rintro ⟨x, h_inf, rfl⟩ obtain ⟨φ, h_mono, h_x⟩ := frequently_iff_strict_mono.mp h_inf apply frequently_iff_strict_mono.mpr aesop · intro h_inf let s := { x : Π i, X i | x i = x_i } have h_inf' : ∃ᶠ k in atTop, xs k ∈ s := by exact h_inf obtain ⟨x, h_x, h_inf''⟩ := frequently_in_finite_set.mp h_inf' aesop- Project
- Automata Theory
- License
- Apache-2.0
- Commit
- f196548710ce
- Source
- AutomataTheory/Sequences/InfOcc.lean:86-97
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Related declarations
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acc_lang_congr
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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.
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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.