Da concat ptr2 antitone
Automata.da_concat_ptr2_antitone
Plain-language statement
The value of DA.ConcatPtr2 is a non-increasing over time.
Exact Lean statement
theorem da_concat_ptr2_antitone (as : Stream' A) (n : ℕ) (h_n : M1.DetRun as n ∈ acc1):
Antitone (DA.ConcatPtr2 M1 acc1 M2 as n h_n)Formal artifact
Lean source
theorem da_concat_ptr2_antitone (as : Stream' A) (n : ℕ) (h_n : M1.DetRun as n ∈ acc1): Antitone (DA.ConcatPtr2 M1 acc1 M2 as n h_n) := by apply antitone_nat_of_succ_le ; intro k have h_spec_k1 := choose_spec (da_concat_ptr2_exists M1 acc1 M2 as n h_n (k + 1)) have h_def_k1 : M1.ConcatPtr2 acc1 M2 as n h_n (k + 1) = choose (da_concat_ptr2_exists M1 acc1 M2 as n h_n (k + 1)) := rfl simp [← h_def_k1, ← add_assoc] at h_spec_k1 obtain ⟨_, h_eq1, h_min⟩ := h_spec_k1 by_contra! h_contra have h_eq2 := h_min (M1.ConcatPtr2 acc1 M2 as n h_n k) (by fin_omega) simp [da_concat_ptr2_det_run, h_eq1] at h_eq2- Project
- Automata Theory
- License
- Apache-2.0
- Commit
- f196548710ce
- Source
- AutomataTheory/Automata/DetConcat.lean:203-212
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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.