src/HOL/IOA/meta_theory/Solve.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/IOA/meta_theory/Solve.ML	Mon Mar 20 15:37:03 1995 +0100
@@ -0,0 +1,45 @@
+(*  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);
+
+  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";