Theory Stop

(*<*)
―‹ ******************************************************************** 
 * 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)
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 * This file       : A Combined CSP Theory
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section‹ The STOP Process ›

theory     Stop
imports    Process 
begin 

lift_definition STOP :: ‹'α process›
  is ‹({(s, X). s = []}, {})›
  unfolding is_process_def FAILURES_def DIVERGENCES_def by simp


lemma F_STOP : "ℱ STOP = {(s,X). s = []}"
  by (simp add: FAILURES_def Failures.rep_eq STOP.rep_eq)

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

lemma T_STOP: "𝒯 STOP = {[]}"
  by (simp add: Traces.rep_eq TRACES_def Failures.rep_eq[symmetric] F_STOP)


lemma STOP_iff_T: ‹P = STOP ⟷ 𝒯 P = {[]}›
  apply (intro iffI, simp add: T_STOP)
  apply (subst Process_eq_spec, safe, simp_all add: F_STOP D_STOP)
  by (use F_T in force, use is_processT5_S7 in fastforce)
     (metis D_T append_Nil front_tickFree_single is_processT7_S
            list.distinct(1) singletonD tickFree_Nil)





end