IOA/meta_theory/Solve.ML

replaced 'val ... = result()' by 'qed "..."'

(*  Title:      HOL/IOA/meta_theory/Solve.ML
    ID:         $Id$
    Author:     Tobias Nipkow & Konrad Slind
    Copyright   1994  TU Muenchen

Weak possibilities mapping (abstraction)
*)

open Solve;

val SS = SS addsimps [mk_behaviour_thm,trans_in_actions];

goalw Solve.thy [is_weak_pmap_def,behaviours_def]
  "!!f. [| IOA(C); IOA(A); externals(asig_of(C)) = externals(asig_of(A)); \
\          is_weak_pmap(f,C,A) |] ==> behaviours(C) <= behaviours(A)";

  by (simp_tac(SS addsimps [has_behaviour_def])1);
  by (safe_tac set_cs);

  (* give execution of abstract automata *)
  by (res_inst_tac[("x","<mk_behaviour(A,fst(ex)),%i.f(snd(ex,i))>")] bexI 1);

  (* Behaviours coincide *)
  by (asm_simp_tac (SS addsimps [mk_behaviour_def,filter_oseq_idemp])1);

  (* Use lemma *)
  by (forward_tac [states_of_exec_reachable] 1);

  (* Now show that it's an execution *)
  by (asm_full_simp_tac(SS addsimps [executions_def]) 1);
  by (safe_tac set_cs);

  (* Start states map to start states *)
  by (dtac bspec 1);
  by (atac 1);

  (* Show that it's an execution fragment *)
  by (asm_full_simp_tac (SS addsimps [is_execution_fragment_def])1);
  by (safe_tac HOL_cs);

  (* Cases on whether action is external or not (basically) *)
  (* 1 *)
  by (eres_inst_tac [("x","snd(ex,n)")] allE 1);
  by (eres_inst_tac [("x","snd(ex,Suc(n))")] allE 1);
  by (eres_inst_tac [("x","aa")] allE 1);
  by (asm_full_simp_tac SS 1);

  (* 2 *)
  by (eres_inst_tac [("x","snd(ex,n)")] allE 1);
  by (eres_inst_tac [("x","snd(ex,Suc(n))")] allE 1);
  by (eres_inst_tac [("x","a")] allE 1);
  by (asm_full_simp_tac SS 1);
qed "trace_inclusion";