Require Import Coq.Lists.List. Require Import Coq.Strings.Ascii. Require Import Turing.Lang. Require Import Turing.Regular. Require Import Turing.Regex. Import ListNotations. Import RegexNotations. Import Lang.LangNotations. Open Scope char_scope. Open Scope lang_scope. Open Scope regex_scope. (* ---------------------- END OF PREAMBLE ------------------ *) Definition L1 := "1" ;; (r_star "1";; ("0";; r_star "0")). Lemma l1_pump: In ["1"; "0"; "0"] (Pump (Accept L1) 3). Proof. apply pump_def with (x:=["1"; "0"]) (y:=["0"]) (z:=[]). - reflexivity. - intros N. inversion N. - auto. - intros. unfold In. unfold L1. Search (r_char _ ;; _). apply accept_cons. Search (r_star _ ;; _). apply accept_app_star_skip. Search (_ ++ []). rewrite app_nil_r. apply accept_cons. Search (Util.pow _ _ \in _). apply accept_pow_char. Qed.