Theory Skip

(*<*)
―‹ ******************************************************************** 
 * Project         : HOL-CSP - A Shallow Embedding of CSP in  Isabelle/HOL
 * Version         : 2.0
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 * Author          : Burkhart Wolff.
 *                   (Based on HOL-CSP 1.0 by Haykal Tej and Burkhart Wolff)
 *
 * This file       : A Combined CSP Theory
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section‹The SKIP Process›

theory Skip
imports Process
begin

lift_definition SKIP :: ‹'α process›
  is ‹({(s, X). s = [] ∧ tick ∉ X} ∪ {(s, X). s = [tick]}, {})›
  unfolding is_process_def FAILURES_def DIVERGENCES_def
  by (auto simp add: append_eq_Cons_conv)


lemma F_SKIP:
  "ℱ SKIP = {(s, X). s = [] ∧ tick ∉ X} ∪ {(s, X). s = [tick]}"
  by (simp add: FAILURES_def Failures.rep_eq SKIP.rep_eq)

lemma D_SKIP: "𝒟 SKIP = {}"
  by (simp add: DIVERGENCES_def Divergences.rep_eq SKIP.rep_eq)

lemma T_SKIP: "𝒯 SKIP ={[], [tick]}"
  by (auto simp add: Traces.rep_eq TRACES_def Failures.rep_eq[symmetric] F_SKIP)


end