# HG changeset patch
# User paulson
# Date 912678306 -3600
# Node ID 1894bfc4aee96c30423d08655c5a70d87833fdc4
# Parent  c48050d6928dc73d2036f57233f29bdf2bd1064f
Addition of the States component; parts of Comp not working

diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Client.ML
--- a/src/HOL/UNITY/Client.ML	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Client.ML	Thu Dec 03 10:45:06 1998 +0100
@@ -90,7 +90,8 @@
 
 (*** Towards proving the liveness property ***)
 
-Goal "Cli_prg Join G   \
+Goal "States Cli_prg = States G \
+\     ==> Cli_prg Join G   \
 \       : transient {s. size (giv s) = Suc k &  \
 \                       size (rel s) = k & ask s ! k <= giv s ! k}";
 by (res_inst_tac [("act", "rel_act")] transient_mem 1);
@@ -130,11 +131,13 @@
 by (Clarify_tac 1);
 by (rtac Stable_transient_reachable_LeadsTo 1);
 by (res_inst_tac [("k", "k")] transient_lemma 2);
+be Disjoint_States_eq 2;
 by (force_tac (claset() addDs [impOfSubs Increasing_size,
 			       impOfSubs Increasing_Stable_less],
 	       simpset()) 1);
 by (rtac (make_elim (lemma1 RS guaranteesD)) 1);
  by (Blast_tac 1);
+be Disjoint_States_eq 1;
 by (auto_tac (claset(),
 	      simpset() addsimps [Invariant_eq_always, giv_meets_ask_def]));
 by (ALLGOALS Force_tac);
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Client.thy
--- a/src/HOL/UNITY/Client.thy	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Client.thy	Thu Dec 03 10:45:06 1998 +0100
@@ -48,7 +48,8 @@
 		          size (ask s) = size (rel s))}"
 
   Cli_prg :: state program
-    "Cli_prg == mk_program ({s. tok s : atMost Max &
+    "Cli_prg == mk_program (UNIV,
+			    {s. tok s : atMost Max &
 			        giv s = [] &
 			        ask s = [] &
 			        rel s = []},
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Common.ML
--- a/src/HOL/UNITY/Common.ML	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Common.ML	Thu Dec 03 10:45:06 1998 +0100
@@ -30,13 +30,13 @@
 
 (*** Some programs that implement the safety property above ***)
 
-Goal "SKIP : constrains {m} (maxfg m)";
+Goal "SKIP UNIV : constrains {m} (maxfg m)";
 by (simp_tac (simpset() addsimps [constrains_def, maxfg_def, le_max_iff_disj,
 				  fasc]) 1);
 result();
 
 (*This one is  t := ftime t || t := gtime t*)
-Goal "mk_program (UNIV, {range(%t.(t,ftime t)), range(%t.(t,gtime t))}) \
+Goal "mk_program (UNIV, UNIV, {range(%t.(t,ftime t)), range(%t.(t,gtime t))}) \
 \      : constrains {m} (maxfg m)";
 by (simp_tac (simpset() addsimps [constrains_def, maxfg_def, 
 				  le_max_iff_disj, fasc]) 1);
@@ -44,7 +44,7 @@
 result();
 
 (*This one is  t := max (ftime t) (gtime t)*)
-Goal "mk_program (UNIV, {range(%t.(t, max (ftime t) (gtime t)))}) \
+Goal "mk_program (UNIV, UNIV, {range(%t.(t, max (ftime t) (gtime t)))}) \
 \      : constrains {m} (maxfg m)";
 by (simp_tac 
     (simpset() addsimps [constrains_def, maxfg_def, max_def, gasc]) 1);
@@ -52,7 +52,8 @@
 result();
 
 (*This one is  t := t+1 if t <max (ftime t) (gtime t) *)
-Goal "mk_program (UNIV, { {(t, Suc t) | t. t < max (ftime t) (gtime t)} }) \
+Goal "mk_program (UNIV, UNIV, \
+\                 { {(t, Suc t) | t. t < max (ftime t) (gtime t)} }) \
 \      : constrains {m} (maxfg m)";
 by (simp_tac 
     (simpset() addsimps [constrains_def, maxfg_def, max_def, gasc]) 1);
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Comp.ML
--- a/src/HOL/UNITY/Comp.ML	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Comp.ML	Thu Dec 03 10:45:06 1998 +0100
@@ -16,68 +16,83 @@
 
 (*** component ***)
 
-Goalw [component_def] "component SKIP F";
-by (blast_tac (claset() addIs [Join_SKIP_left]) 1);
+Goalw [component_def] "component (SKIP (States F)) F";
+by (force_tac (claset() addIs [Join_SKIP_left], simpset()) 1);
 qed "component_SKIP";
 
 Goalw [component_def] "component F F";
-by (blast_tac (claset() addIs [Join_SKIP_right]) 1);
+by (force_tac (claset() addIs [Join_SKIP_right], simpset()) 1);
 qed "component_refl";
 
 AddIffs [component_SKIP, component_refl];
 
-Goalw [component_def] "component F (F Join G)";
+Goalw [component_def] "States F = States G ==> component F (F Join G)";
 by (Blast_tac 1);
 qed "component_Join1";
 
-Goalw [component_def] "component G (F Join G)";
+Goalw [component_def] "States F = States G ==> component G (F Join G)";
 by (simp_tac (simpset() addsimps [Join_commute]) 1);
+by (dtac sym 1);
 by (Blast_tac 1);
 qed "component_Join2";
 
-Goalw [component_def] "i : I ==> component (F i) (JN i:I. (F i))";
-by (blast_tac (claset() addIs [JN_absorb]) 1);
+Goalw [component_def, eqStates_def] 
+    "[| i : I;  eqStates I F |] ==> component (F i) (JN i:I. (F i))";
+by (force_tac (claset() addIs [JN_absorb], simpset()) 1);
 qed "component_JN";
 
 Goalw [component_def] "[| component F G; component G H |] ==> component F H";
-by (blast_tac (claset() addIs [Join_assoc RS sym]) 1);
+by (force_tac (claset() addIs [Join_assoc RS sym], simpset()) 1);
 qed "component_trans";
 
-Goalw [component_def,Join_def] "component F G ==> Acts F <= Acts G";
-by Auto_tac;
+Goalw [component_def] "component F G ==> Acts F <= Acts G";
+by (force_tac (claset(), simpset() addsimps [Acts_Join]) 1);
 qed "component_Acts";
 
 Goalw [component_def,Join_def] "component F G ==> Init G <= Init F";
 by Auto_tac;
 qed "component_Init";
 
+Goalw [component_def] "component F G ==> States F = States G";
+by Auto_tac;
+qed "component_States";
+
 Goal "[| component F G; component G F |] ==> F=G";
-by (asm_simp_tac (simpset() addsimps [program_equalityI, equalityI, 
-				      component_Acts, component_Init]) 1);
+by (blast_tac (claset() addSIs [program_equalityI, component_States, 
+				component_Init, component_Acts]) 1);
 qed "component_anti_sym";
 
 Goalw [component_def]
       "component F H = (EX G. F Join G = H & Disjoint F G)";
-by (blast_tac (claset() addSIs [Diff_Disjoint, Join_Diff2]) 1);
+by (blast_tac (claset() addSIs [Disjoint_States_eq, 
+				Diff_Disjoint, Join_Diff2]) 1);
 qed "component_eq";
 
 (*** existential properties ***)
 
 Goalw [ex_prop_def]
-     "[| ex_prop X; finite GG |] ==> GG Int X ~= {} --> (JN G:GG. G) : X";
+     "[| ex_prop X;  finite GG |] \
+\     ==> eqStates GG (%x. x) --> GG Int X ~= {} --> (JN G:GG. G) : X";
 by (etac finite_induct 1);
-by (auto_tac (claset(), simpset() addsimps [Int_insert_left]));
+by (Simp_tac 1);
+by (rename_tac "GG J" 1);
+by (full_simp_tac (simpset() addsimps [Int_insert_left]) 1);
+by (dres_inst_tac [("x","J")] spec 1);
+by (Force_tac 1);
 qed_spec_mp "ex1";
 
 Goalw [ex_prop_def]
-     "ALL GG. finite GG & GG Int X ~= {} --> (JN G:GG. G) : X ==> ex_prop X";
+     "ALL GG. finite GG & eqStates GG (%x. x) & GG Int X ~= {} \
+\       --> (JN G:GG. G) : X ==> ex_prop X";
 by (Clarify_tac 1);
 by (dres_inst_tac [("x", "{F,G}")] spec 1);
 by Auto_tac;
 qed "ex2";
 
 (*Chandy & Sanders take this as a definition*)
-Goal "ex_prop X = (ALL GG. finite GG & GG Int X ~= {} --> (JN G:GG. G) : X)";
+Goal "ex_prop X = \
+\       (ALL GG. finite GG & eqStates GG (%x. x) & GG Int X ~= {} \
+\          --> (JN G:GG. G) : X)";
 by (blast_tac (claset() addIs [ex1,ex2]) 1);
 qed "ex_prop_finite";
 
@@ -88,6 +103,7 @@
 by (Blast_tac 1);
 by Safe_tac;
 by (stac Join_commute 2);
+by (dtac sym 2);
 by (ALLGOALS Blast_tac);
 qed "ex_prop_equiv";
 
@@ -95,13 +111,15 @@
 (*** universal properties ***)
 
 Goalw [uv_prop_def]
-     "[| uv_prop X; finite GG |] ==> GG <= X --> (JN G:GG. G) : X";
+     "[| uv_prop X; finite GG |] \
+\     ==> eqStates GG (%x. x) --> GG <= X --> (JN G:GG. G) : X";
 by (etac finite_induct 1);
 by (auto_tac (claset(), simpset() addsimps [Int_insert_left]));
 qed_spec_mp "uv1";
 
 Goalw [uv_prop_def]
-     "ALL GG. finite GG & GG <= X --> (JN G:GG. G) : X  ==> uv_prop X";
+     "ALL GG. finite GG & eqStates GG (%x. x) & GG <= X \
+\       --> (JN G:GG. G) : X  ==> uv_prop X";
 by (rtac conjI 1);
 by (Clarify_tac 2);
 by (dres_inst_tac [("x", "{F,G}")] spec 2);
@@ -110,7 +128,8 @@
 qed "uv2";
 
 (*Chandy & Sanders take this as a definition*)
-Goal "uv_prop X = (ALL GG. finite GG & GG <= X --> (JN G:GG. G) : X)";
+Goal "uv_prop X = (ALL GG. finite GG & eqStates GG (%x. x) & GG <= X \
+\       --> (JN G:GG. G) : X)";
 by (blast_tac (claset() addIs [uv1,uv2]) 1);
 qed "uv_prop_finite";
 
@@ -180,7 +199,8 @@
 qed "guaranteesI";
 
 Goalw [guarantees_def, component_def]
-     "[| F : X guarantees Y;  F Join G : X |] ==> F Join G : Y";
+     "[| F : X guarantees Y;  F Join G : X;  States F = States G |] \
+\     ==> F Join G : Y";
 by (Blast_tac 1);
 qed "guaranteesD";
 
@@ -203,36 +223,46 @@
 
 Goalw [refines_def]
      "[| H refines G wrt X;  G refines F wrt X |] ==> H refines F wrt X";
-by (Blast_tac 1);
+by Auto_tac;
 qed "refines_trans";
 
 Goalw [strict_ex_prop_def]
-     "strict_ex_prop X \
-\     ==> (ALL H. F Join H : X --> G Join H : X) = (F:X --> G:X)";
+     "[| strict_ex_prop X;  States F = States G |] \
+\     ==> (ALL H. States F = States H & F Join H : X --> G Join H : X) = \
+\         (F:X --> G:X)";
+by Safe_tac;
 by (Blast_tac 1);
+auto();
 qed "strict_ex_refine_lemma";
 
 Goalw [strict_ex_prop_def]
-     "strict_ex_prop X \
-\     ==> (ALL H. F Join H : welldef & F Join H : X --> G Join H : X) = \
+     "[| strict_ex_prop X;  States F = States G |] \
+\     ==> (ALL H. States F = States H & F Join H : welldef & F Join H : X \
+\           --> G Join H : X) = \
 \         (F: welldef Int X --> G:X)";
 by Safe_tac;
-by (eres_inst_tac [("x","SKIP"), ("P", "%H. ?PP H --> ?RR H")] allE 1);
+by (eres_inst_tac [("x","SKIP ?A"), ("P", "%H. ?PP H --> ?RR H")] allE 1);
 by (auto_tac (claset() addDs [Join_welldef_D1, Join_welldef_D2], simpset()));
 qed "strict_ex_refine_lemma_v";
 
-Goal "[| strict_ex_prop X;  \
-\        ALL H. F Join H : welldef Int X --> G Join H : welldef |] \
+Goal "[| strict_ex_prop X;  States F = States G;  \
+\        ALL H. States F = States H & F Join H : welldef Int X \
+\          --> G Join H : welldef |] \
 \     ==> (G refines F wrt X) = (G iso_refines F wrt X)";
-by (res_inst_tac [("x","SKIP")] allE 1
+bd sym 1;
+by (res_inst_tac [("x","SKIP (States G)")] allE 1
     THEN assume_tac 1);
 by (asm_full_simp_tac (simpset() addsimps [refines_def, iso_refines_def,
 					   strict_ex_refine_lemma_v]) 1);
 qed "ex_refinement_thm";
 
+
+(***
+
+
 Goalw [strict_uv_prop_def]
      "strict_uv_prop X \
-\     ==> (ALL H. F Join H : X --> G Join H : X) = (F:X --> G:X)";
+\     ==> (ALL H. States F = States H & F Join H : X --> G Join H : X) = (F:X --> G:X)";
 by (Blast_tac 1);
 qed "strict_uv_refine_lemma";
 
@@ -254,3 +284,4 @@
 by (asm_full_simp_tac (simpset() addsimps [refines_def, iso_refines_def,
 					   strict_uv_refine_lemma_v]) 1);
 qed "uv_refinement_thm";
+***)
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Comp.thy
--- a/src/HOL/UNITY/Comp.thy	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Comp.thy	Thu Dec 03 10:45:06 1998 +0100
@@ -16,23 +16,29 @@
     case, proving equivalence with Chandy and Sanders's n-ary definitions*)
 
   ex_prop  :: 'a program set => bool
-   "ex_prop X == ALL F G. F:X | G: X --> (F Join G) : X"
+   "ex_prop X ==
+      ALL F G. (F:X | G: X) & States F = States G --> (F Join G) : X"
 
   strict_ex_prop  :: 'a program set => bool
-   "strict_ex_prop X == ALL F G. (F:X | G: X) = (F Join G : X)"
+   "strict_ex_prop X ==
+      ALL F G. States F = States G --> (F:X | G: X) = (F Join G : X)"
 
   uv_prop  :: 'a program set => bool
-   "uv_prop X == SKIP: X & (ALL F G. F:X & G: X --> (F Join G) : X)"
+   "uv_prop X ==
+      SKIP UNIV : X &
+      (ALL F G. F:X & G: X & States F = States G --> (F Join G) : X)"
 
   strict_uv_prop  :: 'a program set => bool
-   "strict_uv_prop X == SKIP: X & (ALL F G. (F:X & G: X) = (F Join G : X))"
+   "strict_uv_prop X ==
+      SKIP UNIV : X &
+      (ALL F G. States F = States G --> (F:X & G: X) = (F Join G : X))"
 
   (*Ill-defined programs can arise through "Join"*)
   welldef :: 'a program set  
    "welldef == {F. Init F ~= {}}"
 
   component :: ['a program, 'a program] => bool
-   "component F H == EX G. F Join G = H"
+   "component F H == EX G. F Join G = H & States F = States G"
 
   guarantees :: ['a program set, 'a program set] => 'a program set (infixl 65)
    "X guarantees Y == {F. ALL H. component F H --> H:X --> H:Y}"
@@ -40,7 +46,9 @@
   refines :: ['a program, 'a program, 'a program set] => bool
 			("(3_ refines _ wrt _)" [10,10,10] 10)
    "G refines F wrt X ==
-      ALL H. (F Join H) : welldef Int X --> G Join H : welldef Int X"
+      States F = States G &
+      (ALL H. States F = States H & (F Join H) : welldef Int X
+        --> G Join H : welldef Int X)"
 
   iso_refines :: ['a program, 'a program, 'a program set] => bool
 			("(3_ iso'_refines _ wrt _)" [10,10,10] 10)
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Constrains.ML
--- a/src/HOL/UNITY/Constrains.ML	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Constrains.ML	Thu Dec 03 10:45:06 1998 +0100
@@ -89,19 +89,27 @@
 by (blast_tac (claset() addIs [constrains_weaken]) 1);
 qed "ball_Constrains_INT";
 
-Goal "F : Constrains A A' ==> reachable F Int A <= A'";
+Goal "[| F : Constrains A A'; A <= reachable F |] ==> A <= A'";
 by (asm_full_simp_tac (simpset() addsimps [Constrains_def]) 1);
 by (dtac constrains_imp_subset 1);
-by (ALLGOALS
-    (full_simp_tac (simpset() addsimps [Int_subset_iff, Int_lower1])));
+by (auto_tac (claset() addIs [impOfSubs reachable_subset_States],
+	      simpset() addsimps [Int_subset_iff, Int_lower1]));
 qed "Constrains_imp_subset";
 
 Goalw [Constrains_def]
     "[| F : Constrains A B; F : Constrains B C |]   \
 \    ==> F : Constrains A C";
-by (blast_tac (claset() addIs [constrains_trans, constrains_weaken]) 1);
+by (blast_tac (claset() addIs [impOfSubs reachable_subset_States,
+			       constrains_trans, constrains_weaken]) 1);
 qed "Constrains_trans";
 
+Goal "[| F : Constrains A (A' Un B); F : Constrains B B' |] \
+\     ==> F : Constrains A (A' Un B')";
+by (asm_full_simp_tac (simpset() addsimps [Constrains_def, Int_Un_distrib]) 1);
+by (blast_tac (claset() addIs [impOfSubs reachable_subset_States,
+			       constrains_cancel]) 1);
+qed "Constrains_cancel";
+
 
 (*** Stable ***)
 
@@ -193,13 +201,6 @@
 by (Blast_tac 1);
 qed "Elimination_sing";
 
-Goalw [Constrains_def, constrains_def]
-   "[| F : Constrains A (A' Un B); F : Constrains B B' |] \
-\   ==> F : Constrains A (A' Un B')";
-by (Clarify_tac 1);
-by (Blast_tac 1);
-qed "Constrains_cancel";
-
 
 (*** Specialized laws for handling Invariants ***)
 
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Handshake.ML
--- a/src/HOL/UNITY/Handshake.ML	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Handshake.ML	Thu Dec 03 10:45:06 1998 +0100
@@ -11,6 +11,7 @@
 (*split_all_tac causes a big blow-up*)
 claset_ref() := claset() delSWrapper record_split_name;
 
+Addsimps [F_def RS def_prg_States, G_def RS def_prg_States];
 Addsimps [F_def RS def_prg_Init, G_def RS def_prg_Init];
 program_defs_ref := [F_def, G_def];
 
@@ -20,7 +21,6 @@
 Addsimps (thms"state.update_defs");
 Addsimps [simp_of_set invFG_def];
 
-
 Goal "(F Join G) : Invariant invFG";
 by (rtac InvariantI 1);
 by (Force_tac 1);
@@ -36,12 +36,14 @@
 by (rtac (ensures_stable_Join1 RS leadsTo_Basis RS leadsTo_imp_LeadsTo) 1);
 by (ensures_tac "cmdG" 2);
 by (constrains_tac 1);
+by Auto_tac;
 qed "lemma2_1";
 
 Goal "(F Join G) : LeadsTo ({s. NF s = k} Int {s. BB s}) {s. k < NF s}";
 by (rtac (ensures_stable_Join2 RS leadsTo_Basis RS leadsTo_imp_LeadsTo) 1);
 by (constrains_tac 2);
 by (ensures_tac "cmdF" 1);
+by Auto_tac;
 qed "lemma2_2";
 
 
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Handshake.thy
--- a/src/HOL/UNITY/Handshake.thy	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Handshake.thy	Thu Dec 03 10:45:06 1998 +0100
@@ -21,14 +21,14 @@
     "cmdF == {(s,s'). s' = s (|NF:= Suc(NF s), BB:=False|) & BB s}"
 
   F :: "state program"
-    "F == mk_program ({s. NF s = 0 & BB s}, {cmdF})"
+    "F == mk_program (UNIV, {s. NF s = 0 & BB s}, {cmdF})"
 
   (*G's program*)
   cmdG :: "(state*state) set"
     "cmdG == {(s,s'). s' = s (|NG:= Suc(NG s), BB:=True|) & ~ BB s}"
 
   G :: "state program"
-    "G == mk_program ({s. NG s = 0 & BB s}, {cmdG})"
+    "G == mk_program (UNIV, {s. NG s = 0 & BB s}, {cmdG})"
 
   (*the joint invariant*)
   invFG :: "state set"
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Lift.thy
--- a/src/HOL/UNITY/Lift.thy	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Lift.thy	Thu Dec 03 10:45:06 1998 +0100
@@ -116,7 +116,8 @@
 
   Lprg :: state program
     (*for the moment, we OMIT button_press*)
-    "Lprg == mk_program ({s. floor s = Min & ~ up s & move s & stop s &
+    "Lprg == mk_program (UNIV,
+			 {s. floor s = Min & ~ up s & move s & stop s &
 		          ~ open s & req s = {}},
 			 {request_act, open_act, close_act,
 			  req_up, req_down, move_up, move_down})"
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Mutex.thy
--- a/src/HOL/UNITY/Mutex.thy	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Mutex.thy	Thu Dec 03 10:45:06 1998 +0100
@@ -52,7 +52,8 @@
     "cmd4V == {(s,s'). s' = s (|PP:=False, NN:=#0|) & NN s = #4}"
 
   Mprg :: state program
-    "Mprg == mk_program ({s. ~ UU s & ~ VV s & MM s = #0 & NN s = #0},
+    "Mprg == mk_program (UNIV,
+			 {s. ~ UU s & ~ VV s & MM s = #0 & NN s = #0},
 			 {cmd0U, cmd1U, cmd2U, cmd3U, cmd4U, 
 			  cmd0V, cmd1V, cmd2V, cmd3V, cmd4V})"
 
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/NSP_Bad.thy
--- a/src/HOL/UNITY/NSP_Bad.thy	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/NSP_Bad.thy	Thu Dec 03 10:45:06 1998 +0100
@@ -54,6 +54,6 @@
 constdefs
   Nprg :: state program
     (*Initial trace is empty*)
-    "Nprg == mk_program({[]}, {Fake, NS1, NS2, NS3})"
+    "Nprg == mk_program(UNIV, {[]}, {Fake, NS1, NS2, NS3})"
 
 end
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/PPROD.ML
--- a/src/HOL/UNITY/PPROD.ML	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/PPROD.ML	Thu Dec 03 10:45:06 1998 +0100
@@ -4,11 +4,6 @@
     Copyright   1998  University of Cambridge
 *)
 
-	Addsimps [image_id];
-
-
-val rinst = read_instantiate_sg (sign_of thy);
-
 (*** General lemmas ***)
 
 Goal "x:C ==> (A Times C <= B Times C) = (A <= B)";
@@ -23,9 +18,9 @@
 by (Blast_tac 1);
 qed "Times_Union2";
 
-Goal "Domain (Union S) = (UN A:S. Domain A)";
-by (Blast_tac 1);
-qed "Domain_Union";
+    Goal "Domain (Union S) = (UN A:S. Domain A)";
+    by (Blast_tac 1);
+    qed "Domain_Union";
 
 (** RTimes: the product of two relations **)
 
@@ -65,17 +60,6 @@
 qed "Image_RTimes"; 
 
 
-Goal "- (UNIV Times A) = UNIV Times (-A)";
-by Auto_tac;
-qed "Compl_Times_UNIV1"; 
-
-Goal "- (A Times UNIV) = (-A) Times UNIV";
-by Auto_tac;
-qed "Compl_Times_UNIV2"; 
-
-Addsimps [Compl_Times_UNIV1, Compl_Times_UNIV2]; 
-
-
 (**** Lcopy ****)
 
 (*** Basic properties ***)
@@ -84,9 +68,9 @@
 by (simp_tac (simpset() addsimps [Lcopy_def]) 1);
 qed "Init_Lcopy";
 
-Goal "Id : (%act. act RTimes Id) `` Acts F";
+Goal "diag (States F Times UNIV) : (%act. act RTimes diag UNIV) `` Acts F";
 by (rtac image_eqI 1);
-by (rtac Id_in_Acts 2);
+by (rtac diag_in_Acts 2);
 by Auto_tac;
 val lemma = result();
 
@@ -234,7 +218,7 @@
 Addsimps [Init_lift_prog];
 
 Goalw [lift_prog_def] "Acts (lift_prog i F) = lift_act i `` Acts F";
-by (auto_tac (claset() addIs [Id_in_Acts RSN (2,image_eqI)], simpset()));
+by (auto_tac (claset() addIs [diag_in_Acts RSN (2,image_eqI)], simpset()));
 qed "Acts_lift_prog";
 
 Goalw [PPROD_def] "Init (PPROD I F) = {f. ALL i:I. f i : Init (F i)}";
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/PPROD.thy
--- a/src/HOL/UNITY/PPROD.thy	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/PPROD.thy	Thu Dec 03 10:45:06 1998 +0100
@@ -3,7 +3,7 @@
     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     Copyright   1998  University of Cambridge
 
-General products of programs (Pi operation).
+General products of programs (Pi operation), for replicating components.
 Also merging of state sets.
 *)
 
@@ -11,7 +11,7 @@
 
 constdefs
   (*Cartesian product of two relations*)
-  RTimes :: "[('a*'a) set, ('b*'b) set] => (('a*'b) * ('a*'b)) set"
+  RTimes :: "[('a*'b) set, ('c*'d) set] => (('a*'c) * ('b*'d)) set"
 	("_ RTimes _" [81, 80] 80)
 
     "R RTimes S == {((x,y),(x',y')). (x,x'):R & (y,y'):S}"
@@ -26,8 +26,9 @@
     "fst_act act == (%((x,y),(x',y')). (x,x')) `` act"
 
   Lcopy :: "'a program => ('a*'b) program"
-    "Lcopy F == mk_program (Init F Times UNIV,
-			    (%act. act RTimes Id) `` Acts F)"
+    "Lcopy F == mk_program (UNIV,
+			    Init F Times UNIV,
+			    (%act. act RTimes (diag UNIV)) `` Acts F)"
 
   lift_act :: "['a, ('b*'b) set] => (('a=>'b) * ('a=>'b)) set"
     "lift_act i act == {(f,f'). EX s'. f' = f(i:=s') & (f i, s') : act}"
@@ -36,7 +37,8 @@
     "drop_act i act == (%(f,f'). (f i, f' i)) `` act"
 
   lift_prog :: "['a, 'b program] => ('a => 'b) program"
-    "lift_prog i F == mk_program ({f. f i : Init F}, lift_act i `` Acts F)"
+    "lift_prog i F ==
+       mk_program (UNIV, {f. f i : Init F}, lift_act i `` Acts F)"
 
   (*products of programs*)
   PPROD  :: ['a set, 'a => 'b program] => ('a => 'b) program
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/ROOT.ML
--- a/src/HOL/UNITY/ROOT.ML	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/ROOT.ML	Thu Dec 03 10:45:06 1998 +0100
@@ -11,6 +11,8 @@
 writeln"Root file for HOL/UNITY";
 set proof_timing;
 
+
+
 loadpath := "../Lex" :: !loadpath;   (*to find Prefix.thy*)
 time_use_thy"UNITY";
 
@@ -27,7 +29,9 @@
 time_use_thy "Lift";
 time_use_thy "Comp";
 time_use_thy "Client";
-time_use_thy "PPROD";
+(**
+time_use_thy "PPX";
+**)
 
 loadpath := "../Auth" :: !loadpath;  (*to find Public.thy*)
 use_thy"NSP_Bad";
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Reach.thy
--- a/src/HOL/UNITY/Reach.thy	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Reach.thy	Thu Dec 03 10:45:06 1998 +0100
@@ -24,7 +24,7 @@
     "asgt u v == {(s,s'). s' = s(v:= s u | s v)}"
 
   Rprg :: state program
-    "Rprg == mk_program ({%v. v=init}, UN (u,v): edges. {asgt u v})"
+    "Rprg == mk_program (UNIV, {%v. v=init}, UN (u,v): edges. {asgt u v})"
 
   reach_invariant :: state set
     "reach_invariant == {s. (ALL v. s v --> (init, v) : edges^*) & s init}"
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Traces.ML
--- a/src/HOL/UNITY/Traces.ML	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Traces.ML	Thu Dec 03 10:45:06 1998 +0100
@@ -12,73 +12,161 @@
 
 (*** The abstract type of programs ***)
 
+Goalw [restrict_rel_def] "restrict_rel A Id = diag A";
+by (Blast_tac 1);
+qed "restrict_rel_Id";
+Addsimps [restrict_rel_Id];
+
+Goalw [restrict_rel_def] "restrict_rel A (diag B) = diag (A Int B)";
+by (Blast_tac 1);
+qed "restrict_rel_diag";
+Addsimps [restrict_rel_diag];
+
+Goalw [restrict_rel_def]
+    "restrict_rel A (restrict_rel B r) = restrict_rel (A Int B) r";
+by (Blast_tac 1);
+qed "restrict_rel_restrict_rel";
+Addsimps [restrict_rel_restrict_rel];
+
+Goalw [restrict_rel_def] "restrict_rel A r <= A Times A";
+by (Blast_tac 1);
+qed "restrict_rel_subset";
+Addsimps [restrict_rel_subset];
+
+Goalw [restrict_rel_def]
+    "((x,y) : restrict_rel A r) = ((x,y): r & x: A & y: A)";
+by (Blast_tac 1);
+qed "restrict_rel_iff";
+Addsimps [restrict_rel_iff];
+
+Goalw [restrict_rel_def] "r <= A Times A ==> restrict_rel A r = r";
+by (Blast_tac 1);
+qed "restrict_rel_eq";
+Addsimps [restrict_rel_eq];
+
+Goal "acts <= Pow (A Times A) ==> restrict_rel A `` acts = acts";
+by Auto_tac;
+by (rtac image_eqI 1);
+by (assume_tac 2);
+by (set_mp_tac 1);
+by (Force_tac 1);
+qed "restrict_rel_image";
+
+Goalw [restrict_rel_def] "Domain (restrict_rel A r) <= A Int Domain r";
+by (Blast_tac 1);
+qed "Domain_restrict_rel";
+
+Goalw [restrict_rel_def] "restrict_rel A r ^^ B <= A Int (r ^^ B)";
+by (Blast_tac 1);
+qed "Image_restrict_rel";
+
+Addsimps [diag_iff];
+
 val rep_ss = simpset() addsimps 
-                [Init_def, Acts_def, mk_program_def, Program_def, Rep_Program, 
+                [Int_lower1, image_subset_iff, diag_subset_Times,
+		 States_def, Init_def, Acts_def, 
+		 mk_program_def, Program_def, Rep_Program, 
 		 Rep_Program_inverse, Abs_Program_inverse];
 
 
-Goal "Id: Acts F";
+(** Basic laws guaranteed by the abstract type "program" **)
+
+Goal "Init F <= States F";
 by (cut_inst_tac [("x", "F")] Rep_Program 1);
 by (auto_tac (claset(), rep_ss));
-qed "Id_in_Acts";
-AddIffs [Id_in_Acts];
+qed "Init_subset_States";
+
+Goal "Acts F <= Pow(States F Times States F)";
+by (cut_inst_tac [("x", "F")] Rep_Program 1);
+by (force_tac (claset(),rep_ss) 1);
+qed "Acts_subset_Pow_States";
+
+Goal "diag (States F) : Acts F";
+by (cut_inst_tac [("x", "F")] Rep_Program 1);
+by (auto_tac (claset(), rep_ss));
+qed "diag_in_Acts";
+AddIffs [diag_in_Acts];
 
 
-Goal "Init (mk_program (init,acts)) = init";
+(** Inspectors for type "program" **)
+
+Goal "States (mk_program (states,init,acts)) = states";
+by (auto_tac (claset(), rep_ss));
+qed "States_eq";
+
+Goal "Init (mk_program (states,init,acts)) = states Int init";
 by (auto_tac (claset(), rep_ss));
 qed "Init_eq";
 
-Goal "Acts (mk_program (init,acts)) = insert Id acts";
+Goal "Acts (mk_program (states,init,acts)) = \
+\     insert (diag states) (restrict_rel states `` acts)";
 by (auto_tac (claset(), rep_ss));
+qed "Acts_eq_raw";
+
+Goal "acts <= Pow(states Times states) \
+\     ==> Acts (mk_program (states,init,acts)) = insert (diag states) acts";
+by (asm_simp_tac (simpset() addsimps [Acts_eq_raw, restrict_rel_image]) 1);
 qed "Acts_eq";
 
-Addsimps [Acts_eq, Init_eq];
+Addsimps [States_eq, Acts_eq, Init_eq];
 
 
-Goal "[| Init F = Init G; Acts F = Acts G |] ==> F = G";
-by (cut_inst_tac [("p", "Rep_Program F")] surjective_pairing 1);
+(** The notation of equality for type "program" **)
+
+Goal "[| States F = States G; Init F = Init G; Acts F = Acts G |] ==> F = G";
+by (subgoals_tac ["EX x. Rep_Program F = x",
+		  "EX x. Rep_Program G = x"] 1);
+by (REPEAT (Blast_tac 2));
+by (Clarify_tac 1);
 by (auto_tac (claset(), rep_ss));
-by (dres_inst_tac [("f", "Abs_Program")] arg_cong 1);
-by (full_simp_tac (rep_ss addsimps [surjective_pairing RS sym]) 1);
+by (REPEAT (dres_inst_tac [("f", "Abs_Program")] arg_cong 1));
+by (asm_full_simp_tac rep_ss 1);
 qed "program_equalityI";
 
 val [major,minor] =
-Goal "[| F = G; [| Init F = Init G; Acts F = Acts G |] ==> P |] ==> P";
+Goal "[| F = G; \
+\        [| States F = States G; Init F = Init G; Acts F = Acts G |] ==> P \
+\     |] ==> P";
 by (rtac minor 1);
 by (auto_tac (claset(), simpset() addsimps [major]));
 qed "program_equalityE";
 
-(*** These rules allow "lazy" definition expansion ***)
+(*** These rules allow "lazy" definition expansion 
+     They avoid expanding the full program, which is a large expression
+***)
 
-(*The program is not expanded, but its Init is*)
-val [rew] = goal thy
-    "[| F == mk_program (init,acts) |] \
-\    ==> Init F = init";
-by (rewtac rew);
+Goal "[| F == mk_program (states,init,acts) |] \
+\     ==> States F = states";
+by Auto_tac;
+qed "def_prg_States";
+
+Goal "[| F == mk_program (states,init,acts); init <= states |] \
+\     ==> Init F = init";
 by Auto_tac;
 qed "def_prg_Init";
 
+Goal "[| F == mk_program (states,init,acts); \
+\        acts <= Pow(states Times states) |] \
+\     ==> Acts F = insert (diag states) acts";
+by (asm_simp_tac (simpset() addsimps [restrict_rel_image]) 1);
+qed "def_prg_Acts";
+
 (*The program is not expanded, but its Init and Acts are*)
-val [rew] = goal thy
-    "[| F == mk_program (init,acts) |] \
-\    ==> Init F = init & Acts F = insert Id acts";
-by (rewtac rew);
-by Auto_tac;
+Goal "[| F == mk_program (states,init,acts); \
+\        init <= states;  acts <= Pow(states Times states) |] \
+\     ==> Init F = init & Acts F = insert (diag states) acts";
+by (asm_simp_tac (HOL_ss addsimps [def_prg_Init, def_prg_Acts]) 1);
 qed "def_prg_simps";
 
 (*An action is expanded only if a pair of states is being tested against it*)
-val [rew] = goal thy
-    "[| act == {(s,s'). P s s'} |] ==> ((s,s') : act) = P s s'";
-by (rewtac rew);
+Goal "[| act == {(s,s'). P s s'} |] ==> ((s,s') : act) = P s s'";
 by Auto_tac;
 qed "def_act_simp";
 
 fun simp_of_act def = def RS def_act_simp;
 
 (*A set is expanded only if an element is being tested against it*)
-val [rew] = goal thy
-    "A == B ==> (x : A) = (x : B)";
-by (rewtac rew);
+Goal "A == B ==> (x : A) = (x : B)";
 by Auto_tac;
 qed "def_set_simp";
 
@@ -87,6 +175,13 @@
 
 (*** traces and reachable ***)
 
+Goal "reachable F <= States F";
+by Safe_tac;
+by (etac reachable.induct 1);
+by (blast_tac (claset() addDs [impOfSubs Acts_subset_Pow_States]) 2);
+by (blast_tac (claset() addIs [impOfSubs Init_subset_States]) 1);
+qed "reachable_subset_States";
+
 Goal "reachable F = {s. EX evs. (s,evs): traces (Init F) (Acts F)}";
 by Safe_tac;
 by (etac traces.induct 2);
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Traces.thy
--- a/src/HOL/UNITY/Traces.thy	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Traces.thy	Thu Dec 03 10:45:06 1998 +0100
@@ -25,17 +25,32 @@
 
 
 typedef (Program)
-  'a program = "{(init:: 'a set, acts :: ('a * 'a)set set). Id:acts}"
+  'a program = "{(states :: 'a set,
+		  init   :: 'a set,
+		  acts   :: ('a * 'a)set set).
+		 init <= states &
+		 acts <= Pow(states Times states) &
+		 diag states : acts}"
 
 constdefs
-    mk_program :: "('a set * ('a * 'a)set set) => 'a program"
-    "mk_program == %(init, acts). Abs_Program (init, insert Id acts)"
+  restrict_rel :: "['a set, ('a * 'a) set] => ('a * 'a) set"
+    "restrict_rel A r == (A Times A) Int r"
 
-    Init :: "'a program => 'a set"
-    "Init F == fst (Rep_Program F)"
+  mk_program :: "('a set * 'a set * ('a * 'a)set set) => 'a program"
+    "mk_program ==
+       %(states, init, acts).
+	Abs_Program (states,
+		     states Int init,
+		     restrict_rel states `` (insert Id acts))"
 
-    Acts :: "'a program => ('a * 'a)set set"
-    "Acts F == snd (Rep_Program F)"
+  States :: "'a program => 'a set"
+    "States F == (%(states, init, acts). states) (Rep_Program F)"
+
+  Init :: "'a program => 'a set"
+    "Init F == (%(states, init, acts). init) (Rep_Program F)"
+
+  Acts :: "'a program => ('a * 'a)set set"
+    "Acts F == (%(states, init, acts). acts) (Rep_Program F)"
 
 
 consts reachable :: "'a program => 'a set"
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/UNITY.ML
--- a/src/HOL/UNITY/UNITY.ML	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/UNITY.ML	Thu Dec 03 10:45:06 1998 +0100
@@ -12,6 +12,29 @@
 HOL_quantifiers := false;
 
 
+(*** General lemmas ***)
+
+    Goal "Pow UNIV = UNIV";
+    by (Blast_tac 1);
+    qed "Pow_UNIV";
+    Addsimps [Pow_UNIV];
+
+Goal "UNIV Times UNIV = UNIV";
+by Auto_tac;
+qed "UNIV_Times_UNIV"; 
+Addsimps [UNIV_Times_UNIV];
+
+Goal "- (UNIV Times A) = UNIV Times (-A)";
+by Auto_tac;
+qed "Compl_Times_UNIV1"; 
+
+Goal "- (A Times UNIV) = (-A) Times UNIV";
+by Auto_tac;
+qed "Compl_Times_UNIV2"; 
+
+Addsimps [Compl_Times_UNIV1, Compl_Times_UNIV2]; 
+
+
 (*** constrains ***)
 
 overload_1st_set "UNITY.constrains";
@@ -83,16 +106,25 @@
 by (Blast_tac 1);
 qed "ball_constrains_INT";
 
-Goalw [constrains_def] "[| F : constrains A A' |] ==> A<=A'";
-by (Blast_tac 1);
+Goalw [constrains_def] "[| F : constrains A A'; A <= States F |] ==> A <= A'";
+by (Force_tac 1);
 qed "constrains_imp_subset";
 
-Goalw [constrains_def]
-    "[| F : constrains A B; F : constrains B C |]   \
+(*The reasoning is by subsets since "constrains" refers to single actions
+  only.  So this rule isn't that useful.*)
+Goal "[| F : constrains A B; F : constrains B C; B <= States F |]   \
 \    ==> F : constrains A C";
-by (Blast_tac 1);
+by (etac constrains_weaken_R 1);
+by (etac constrains_imp_subset 1);
+by (assume_tac 1);
 qed "constrains_trans";
 
+Goal "[| F : constrains A (A' Un B); F : constrains B B'; B <= States F|] \
+\     ==> F : constrains A (A' Un B')";
+by (etac constrains_weaken_R 1);
+by (blast_tac (claset() addDs [impOfSubs constrains_imp_subset]) 1);
+qed "constrains_cancel";
+
 
 (*** stable ***)
 
@@ -212,14 +244,6 @@
 qed "elimination_sing";
 
 
-Goalw [constrains_def]
-   "[| F : constrains A (A' Un B); F : constrains B B' |] \
-\   ==> F : constrains A (A' Un B')";
-by (Clarify_tac 1);
-by (Blast_tac 1);
-qed "constrains_cancel";
-
-
 
 (*** Theoretical Results from Section 6 ***)
 
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Union.ML
--- a/src/HOL/UNITY/Union.ML	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Union.ML	Thu Dec 03 10:45:06 1998 +0100
@@ -8,55 +8,124 @@
 From Misra's Chapter 5: Asynchronous Compositions of Programs
 *)
 
+Goal "k:I ==> (INT i:I. A i) Int A k = (INT i:I. A i)";
+by (Blast_tac 1);
+qed "INT_absorb2";
+
+
+val rinst = read_instantiate_sg (sign_of thy);
+
+Addcongs [UN_cong, INT_cong];
 
 (** SKIP **)
 
-Goal "Init SKIP = UNIV";
+Goal "States (SKIP A) = A";
+by (simp_tac (simpset() addsimps [SKIP_def]) 1);
+qed "States_SKIP";
+
+Goal "Init (SKIP A) = A";
 by (simp_tac (simpset() addsimps [SKIP_def]) 1);
 qed "Init_SKIP";
 
-Goal "Acts SKIP = {Id}";
+Goal "Acts (SKIP A) = {diag A}";
 by (simp_tac (simpset() addsimps [SKIP_def]) 1);
 qed "Acts_SKIP";
 
-Addsimps [Init_SKIP, Acts_SKIP];
+Addsimps [States_SKIP, Init_SKIP, Acts_SKIP];
 
-Goal "reachable SKIP = UNIV";
-by (force_tac (claset() addIs reachable.intrs, simpset()) 1);
+Goal "reachable (SKIP A) = A";
+by (force_tac (claset() addEs [reachable.induct]
+			addIs reachable.intrs, simpset()) 1);
 qed "reachable_SKIP";
 
 Addsimps [reachable_SKIP];
 
 
-(** Join and JN **)
+(** Join **)
+
+Goal "States (F Join G) = States F Int States G";
+by (simp_tac (simpset() addsimps [Join_def]) 1);
+qed "States_Join";
 
 Goal "Init (F Join G) = Init F Int Init G";
-by (simp_tac (simpset() addsimps [Join_def]) 1);
+by (auto_tac (claset() addIs [impOfSubs Init_subset_States],
+	      simpset() addsimps [Join_def]));
 qed "Init_Join";
 
-Goal "Acts (F Join G) = Acts F Un Acts G";
+Goal "States F = States G ==> Acts (F Join G) = Acts F Un Acts G";
+by (subgoal_tac "Acts F Un Acts G <= Pow (States G Times States G)" 1);
+by (blast_tac (claset() addEs [equalityE] 
+                        addDs [impOfSubs Acts_subset_Pow_States]) 2);
 by (auto_tac (claset(), simpset() addsimps [Join_def]));
 qed "Acts_Join";
 
+
+(** JN **)
+
+Goalw [JOIN_def, SKIP_def] "(JN i:{}. F i) = (SKIP UNIV)";
+by Auto_tac;
+qed "JN_empty";
+Addsimps [JN_empty];
+
+Goal "States (JN i:I. F i) = (INT i:I. States (F i))";
+by (simp_tac (simpset() addsimps [JOIN_def]) 1);
+qed "States_JN";
+
 Goal "Init (JN i:I. F i) = (INT i:I. Init (F i))";
-by (simp_tac (simpset() addsimps [JOIN_def]) 1);
+by (auto_tac (claset() addIs [impOfSubs Init_subset_States],
+	      simpset() addsimps [JOIN_def]));
 qed "Init_JN";
 
-Goal "Acts (JN i:I. F i) = insert Id (UN i:I. Acts (F i))";
+Goalw [eqStates_def]
+     "[| i: I;  eqStates I F |] ==> Acts (JN i:I. F i) = (UN i:I. Acts (F i))";
+by (Clarify_tac 1);
+by (subgoal_tac "(UN i:I. Acts (F i)) <= Pow (St Times St)" 1);
+by (blast_tac (claset() addEs [equalityE] 
+                        addDs [impOfSubs Acts_subset_Pow_States]) 2);
 by (auto_tac (claset(), simpset() addsimps [JOIN_def]));
 qed "Acts_JN";
 
-Addsimps [Init_Join, Init_JN];
+Goal "eqStates I F \
+\     ==> Acts (JN i:I. F i) = \
+\         (if I={} then {diag UNIV} else (UN i:I. Acts (F i)))";
+by (force_tac (claset(), simpset() addsimps [Acts_JN]) 1);
+qed "Acts_JN_if";
+
+Addsimps [States_Join, Init_Join, States_JN, Init_JN];
+
 
-Goalw [JOIN_def, SKIP_def] "(JN i:{}. F i) = SKIP";
-by Auto_tac;
-qed "JN_empty";
+Goal "(JN x:insert j I. F x) = (F j) Join (JN x:I. F x)";
+by (rtac program_equalityI 1);
+by (ALLGOALS Asm_simp_tac);
+by (asm_simp_tac 
+    (simpset() addsimps [JOIN_def, Join_def, Acts_eq_raw,
+			 image_UNION, image_Un, image_image, Int_assoc]) 1);
+qed "JN_insert";
+Addsimps[JN_insert];
 
-Goal "(JN x:insert a A. B x) = (B a) Join (JN x:A. B x)";
-by (rtac program_equalityI 1);
-by (ALLGOALS (simp_tac (simpset() addsimps [JOIN_def, Join_def])));
-qed "JN_insert";
-Addsimps[JN_empty, JN_insert];
+Goal "k:I ==> A k Join (JN i:I. A i) = (JN i:I. A i)";
+by (stac (JN_insert RS sym) 1);
+by (asm_simp_tac (simpset() addsimps [insert_absorb]) 1);
+qed "JN_absorb";
+
+
+Goalw [eqStates_def] "eqStates {} F";
+by (Simp_tac 1);
+qed "eqStates_empty";
+
+Goalw [eqStates_def]
+    "[| eqStates I F; States (F i) = (INT i: I. States (F i)) |] \
+\    ==> eqStates (insert i I) F";
+by Auto_tac;
+qed "eqStates_insertI";
+
+Goalw [eqStates_def]
+    "eqStates (insert i I) F = \
+\    (eqStates I F & (I={} | States (F i) = (INT i: I. States (F i))))";
+by Auto_tac;
+qed "eqStates_insert_eq";
+
+Addsimps [eqStates_empty, eqStates_insert_eq];
 
 
 (** Algebraic laws **)
@@ -66,170 +135,224 @@
 qed "Join_commute";
 
 Goal "(F Join G) Join H = F Join (G Join H)";
-by (simp_tac (simpset() addsimps Un_ac@[Join_def, Int_assoc]) 1);
+by (rtac program_equalityI 1);
+by (ALLGOALS (asm_simp_tac (simpset() addsimps Un_ac@[Int_assoc])));
+by (asm_simp_tac 
+    (simpset() addsimps Un_ac@Int_ac@[Join_def, Acts_eq_raw,
+				      image_Un, image_image]) 1);
+by (Blast_tac 1);
 qed "Join_assoc";
  
-Goalw [Join_def, SKIP_def] "SKIP Join F = F";
+Goalw [Join_def, SKIP_def] "States F <= A ==> (SKIP A) Join F = F";
 by (rtac program_equalityI 1);
-by (ALLGOALS (simp_tac (simpset() addsimps [insert_absorb])));
+by (ALLGOALS
+    (asm_simp_tac (simpset() addsimps 
+		   Int_ac@[Acts_subset_Pow_States RS restrict_rel_image, 
+			   Acts_eq_raw, insert_absorb, Int_absorb1])));
+by (blast_tac (claset() addIs [impOfSubs Init_subset_States]) 1);
 qed "Join_SKIP_left";
 
-Goalw [Join_def, SKIP_def] "F Join SKIP = F";
-by (rtac program_equalityI 1);
-by (ALLGOALS (simp_tac (simpset() addsimps [insert_absorb])));
+Goal "States F <= A ==> F Join (SKIP A) = F";
+by (stac Join_commute 1);
+by (asm_simp_tac (simpset() addsimps [Join_SKIP_left]) 1);
 qed "Join_SKIP_right";
 
 Addsimps [Join_SKIP_left, Join_SKIP_right];
 
 Goalw [Join_def] "F Join F = F";
 by (rtac program_equalityI 1);
-by Auto_tac;
+by (ALLGOALS
+    (asm_simp_tac (simpset() addsimps 
+		   [insert_absorb, Acts_subset_Pow_States RS Acts_eq])));
+by (blast_tac (claset() addIs [impOfSubs Init_subset_States]) 1);
 qed "Join_absorb";
 
 Addsimps [Join_absorb];
 
-
-Goal "i : I ==> (JN i:I. A i Join B) = ((JN i:I. A i) Join B)";
-by (auto_tac (claset() addSIs [program_equalityI],
-	      simpset() addsimps [Acts_JN, Acts_Join]));
-qed "JN_Join_miniscope";
-
-Goal "k:I ==> A k Join (JN i:I. A i) = (JN i:I. A i)";
-by (auto_tac (claset() addSIs [program_equalityI],
-	      simpset() addsimps [Acts_JN, Acts_Join]));
-qed "JN_absorb";
-
 Goal "(JN i: I Un J. A i) = ((JN i: I. A i) Join (JN i:J. A i))";
-by (auto_tac (claset() addSIs [program_equalityI],
-	      simpset() addsimps [Acts_JN, Acts_Join]));
+by (rtac program_equalityI 1);
+by (ALLGOALS (asm_simp_tac (simpset() addsimps [INT_Un])));
+by (asm_simp_tac 
+    (simpset() addsimps Int_ac@
+                        [JOIN_def, Join_def, Acts_eq_raw, UN_Un, INT_Un, 
+			 image_UNION, image_Un, image_image]) 1);
 qed "JN_Join";
 
 Goal "i: I ==> (JN i:I. c) = c";
 by (auto_tac (claset() addSIs [program_equalityI],
-	      simpset() addsimps [Acts_JN]));
+	      simpset() addsimps [Acts_JN, eqStates_def]));
 qed "JN_constant";
 
 Goal "(JN i:I. A i Join B i) = (JN i:I. A i)  Join  (JN i:I. B i)";
-by (auto_tac (claset() addSIs [program_equalityI],
-	      simpset() addsimps [Acts_JN, Acts_Join]));
+by (rtac program_equalityI 1);
+by (ALLGOALS (asm_simp_tac (simpset() addsimps [INT_Int_distrib])));
+by (asm_simp_tac 
+    (simpset() addsimps [JOIN_def, Join_def, Acts_eq_raw, image_UNION, 
+			 rinst [("A","%x. States (A x) Int States (B x)")] 
+			     INT_absorb2, 
+			 image_Un, image_image]) 1);
+by (asm_simp_tac (simpset() addsimps [INT_Int_distrib RS sym] @ Int_ac) 1);
+by (Blast_tac 1);
 qed "JN_Join_distrib";
 
+Goal "i : I ==> (JN i:I. A i Join B) = ((JN i:I. A i) Join B)";
+by (asm_simp_tac (simpset() addsimps [JN_Join_distrib, JN_constant]) 1);
+qed "JN_Join_miniscope";
+
 
 (*** Safety: constrains, stable, FP ***)
 
-Goalw [constrains_def, JOIN_def]
-    "i : I ==> \
-\    (JN i:I. F i) : constrains A B = (ALL i:I. F i : constrains A B)";
-by (Simp_tac 1);
-by (Blast_tac 1);
-qed "constrains_JN";
+Goal "[| F : constrains A B;  G : constrains A B |] \
+\     ==> F Join G : constrains A B";
+by (auto_tac (claset(),
+	      simpset() addsimps [constrains_def, Join_def, Acts_eq_raw, 
+				  image_Un]));
+by (REPEAT (force_tac (claset() addSEs [ballE], simpset()) 1));
+qed "constrains_imp_Join_constrains";
 
-Goal "F Join G : constrains A B =  \
-\     (F : constrains A B & G : constrains A B)";
-by (auto_tac
-    (claset(),
-     simpset() addsimps [constrains_def, Join_def]));
+Goal "States F = States G ==> \
+\     F Join G : constrains A B = (F : constrains A B & G : constrains A B)";
+by (auto_tac (claset(), simpset() addsimps [constrains_def, Acts_Join]));
 qed "constrains_Join";
 
-(**FAILS, I think; see 5.4.1, Substitution Axiom.
-   The problem is to relate reachable (F Join G) with 
-   reachable F and reachable G
+Goal "[| i : I;  ALL i:I. F i : constrains A B |] \
+\     ==> (JN i:I. F i) : constrains A B";
+by (full_simp_tac (simpset() addsimps [constrains_def, JOIN_def, Acts_eq_raw, 
+				  image_Un]) 1);
+by Safe_tac;
+by (REPEAT (force_tac (claset() addSEs [ballE], simpset()) 1));
+qed "constrains_imp_JN_constrains";
 
-Goalw [Constrains_def]
-    "(JN i:I. F i) : Constrains A B = (ALL i:I. F i : Constrains A B)";
-by (simp_tac (simpset() addsimps [constrains_JN]) 1);
-by (Blast_tac 1);
-qed "Constrains_JN";
+Goal "[| i : I;  eqStates I F |] \
+\     ==> (JN i:I. F i) : constrains A B = (ALL i:I. F i : constrains A B)";
+by (auto_tac (claset(), simpset() addsimps [constrains_def, Acts_JN]));
+qed "constrains_JN";
+
+    (**FAILS, I think; see 5.4.1, Substitution Axiom.
+       The problem is to relate reachable (F Join G) with 
+       reachable F and reachable G
 
-Goal "F Join G : Constrains A B = (Constrains F A B & Constrains G A B)";
-by (auto_tac
-    (claset(),
-     simpset() addsimps [Constrains_def, constrains_Join]));
-qed "Constrains_Join";
-**)
+    Goalw [Constrains_def]
+	"(JN i:I. F i) : Constrains A B = (ALL i:I. F i : Constrains A B)";
+    by (simp_tac (simpset() addsimps [constrains_JN]) 1);
+    by (Blast_tac 1);
+    qed "Constrains_JN";
 
-Goal "[| F : constrains A A';  G : constrains B B' |] \
+    Goal "F Join G : Constrains A B = (Constrains F A B & Constrains G A B)";
+    by (auto_tac
+	(claset(),
+	 simpset() addsimps [Constrains_def, constrains_Join]));
+    qed "Constrains_Join";
+    **)
+
+Goal "[| F : constrains A A';  G : constrains B B';  States F = States G |] \
 \     ==> F Join G : constrains (A Int B) (A' Un B')";
-by (simp_tac (simpset() addsimps [constrains_Join]) 1);
+by (asm_simp_tac (simpset() addsimps [constrains_Join]) 1);
 by (blast_tac (claset() addIs [constrains_weaken]) 1);
 qed "constrains_Join_weaken";
 
-Goal "i : I ==> \
-\     (JN i:I. F i) : stable A = (ALL i:I. F i : stable A)";
+Goal "[| i : I;  eqStates I F |]  \
+\     ==> (JN i:I. F i) : stable A = (ALL i:I. F i : stable A)";
 by (asm_simp_tac (simpset() addsimps [stable_def, constrains_JN]) 1);
 qed "stable_JN";
 
-Goal "[| ALL i:I. F i : invariant A;  i : I |]  \
+Goal "[| ALL i:I. F i : invariant A;  i : I;  eqStates I F |]  \
 \      ==> (JN i:I. F i) : invariant A";
 by (asm_full_simp_tac (simpset() addsimps [invariant_def, stable_JN]) 1);
 by (Blast_tac 1);
 bind_thm ("invariant_JN_I", ballI RS result());
 
-Goal "F Join G : stable A = \
-\     (F : stable A & G : stable A)";
-by (simp_tac (simpset() addsimps [stable_def, constrains_Join]) 1);
+Goal "States F = States G \
+\     ==> F Join G : stable A = (F : stable A & G : stable A)";
+by (asm_simp_tac (simpset() addsimps [stable_def, constrains_Join]) 1);
 qed "stable_Join";
 
-Goal "[| F : invariant A; G : invariant A |]  \
+Goal "[| F : invariant A; G : invariant A; States F = States G |]  \
 \     ==> F Join G : invariant A";
-by (full_simp_tac (simpset() addsimps [invariant_def, stable_Join]) 1);
+by (asm_full_simp_tac (simpset() addsimps [invariant_def, stable_Join]) 1);
 by (Blast_tac 1);
 qed "invariant_JoinI";
 
-Goal "i : I ==> FP (JN i:I. F i) = (INT i:I. FP (F i))";
+Goal "[| i : I;  eqStates I F |]  \
+\      ==> FP (JN i:I. F i) = (INT i:I. FP (F i))";
 by (asm_simp_tac (simpset() addsimps [FP_def, stable_JN, INTER_def]) 1);
 qed "FP_JN";
 
 
 (*** Progress: transient, ensures ***)
 
-Goal "i : I ==> \
-\   (JN i:I. F i) : transient A = (EX i:I. F i : transient A)";
-by (auto_tac (claset(),
-	      simpset() addsimps [transient_def, JOIN_def]));
+
+Goal "[| (JN i:I. F i) : transient A;  i: I |] ==> EX i:I. F i : transient A";
+by (full_simp_tac (simpset() addsimps [transient_def, JOIN_def, Acts_eq_raw, 
+				  Int_absorb1, restrict_rel_def]) 1);
+by Safe_tac;
+by (REPEAT (blast_tac (claset() addSIs [rev_bexI]) 1));
+qed "transient_JN_imp_transient";
+
+Goal "[| i : I;  eqStates I F |]  \
+\     ==> (JN i:I. F i) : transient A = (EX i:I. F i : transient A)";
+by (auto_tac (claset() addSIs [transient_JN_imp_transient], simpset()));
+by (auto_tac (claset(), simpset() addsimps [transient_def, Acts_JN]));
 qed "transient_JN";
 
-Goal "F Join G : transient A = \
-\     (F : transient A | G : transient A)";
-by (auto_tac (claset(),
-	      simpset() addsimps [bex_Un, transient_def,
-				  Join_def]));
+Goal "F Join G : transient A ==> \
+\     F : transient A | G : transient A";
+by (full_simp_tac (simpset() addsimps [transient_def, Join_def, Acts_eq_raw, 
+				       restrict_rel_def]) 1);
+by Safe_tac;
+(*delete act:Acts F possibility*)
+by (rtac FalseE 3);  
+(*delete act:Acts G possibility*)
+by (thin_tac "~ (EX act:Acts G. ?P act)" 2);
+by (REPEAT (blast_tac (claset() addSIs [rev_bexI]) 1));
+qed "transient_Join_imp_transient";
+
+Goal "States F = States G  \
+\     ==> (F Join G : transient A) = (F : transient A | G : transient A)";
+by (auto_tac (claset() addSIs [transient_Join_imp_transient], simpset()));
+by (auto_tac (claset(), simpset() addsimps [transient_def, Acts_Join]));
 qed "transient_Join";
 
-Goal "i : I ==> \
-\     (JN i:I. F i) : ensures A B = \
-\     ((ALL i:I. F i : constrains (A-B) (A Un B)) & \
-\      (EX i:I. F i : ensures A B))";
+Goal "[| i : I;  eqStates I F |]  \
+\     ==> (JN i:I. F i) : ensures A B = \
+\         ((ALL i:I. F i : constrains (A-B) (A Un B)) & \
+\          (EX i:I. F i : ensures A B))";
 by (auto_tac (claset(),
 	      simpset() addsimps [ensures_def, constrains_JN, transient_JN]));
 qed "ensures_JN";
 
 Goalw [ensures_def]
-     "F Join G : ensures A B =     \
-\     (F : constrains (A-B) (A Un B) & \
-\      G : constrains (A-B) (A Un B) & \
-\      (F : ensures A B | G : ensures A B))";
+     "States F = States G  \
+\     ==> F Join G : ensures A B =     \
+\         (F : constrains (A-B) (A Un B) & \
+\          G : constrains (A-B) (A Un B) & \
+\          (F : ensures A B | G : ensures A B))";
 by (auto_tac (claset(),
 	      simpset() addsimps [constrains_Join, transient_Join]));
 qed "ensures_Join";
 
-Goalw [stable_def, constrains_def, Join_def]
-    "[| F : stable A;  G : constrains A A' |] \
+Goal "[| F : stable A;  G : constrains A A';  \
+\        States F = States G; A <= States G |] \
 \    ==> F Join G : constrains A A'";
-by (asm_full_simp_tac (simpset() addsimps [ball_Un]) 1);
+by (forward_tac [constrains_imp_subset] 1);
+by (assume_tac 1);
+by (asm_full_simp_tac (simpset() addsimps [stable_def, constrains_def,
+					   ball_Un, Acts_Join]) 1);
 by (Blast_tac 1);
 qed "stable_constrains_Join";
 
 (*Premise for G cannot use Invariant because  Stable F A  is weaker than
   G : stable A *)
-Goal "[| F : stable A;  G : invariant A |] ==> F Join G : Invariant A";
-by (full_simp_tac (simpset() addsimps [Invariant_def, invariant_def, 
-				       Stable_eq_stable, stable_Join]) 1);
+Goal "[| F : stable A;  G : invariant A;  \
+\        States F = States G |] ==> F Join G : Invariant A";
+by (asm_full_simp_tac (simpset() addsimps [Invariant_def, invariant_def, 
+					   Stable_eq_stable, stable_Join]) 1);
 by (force_tac(claset() addIs [stable_reachable, stable_Int],
 	      simpset() addsimps [Acts_Join]) 1);
 qed "stable_Join_Invariant";
 
-Goal "[| F : stable A;  G : ensures A B |] ==> F Join G : ensures A B";
+Goal "[| F : stable A;  G : ensures A B;  \
+\        States F = States G |] ==> F Join G : ensures A B";
 by (asm_simp_tac (simpset() addsimps [ensures_Join]) 1);
 by (asm_full_simp_tac (simpset() addsimps [stable_def, ensures_def]) 1);
 by (etac constrains_weaken 1);
@@ -237,35 +360,61 @@
 qed "ensures_stable_Join1";
 
 (*As above, but exchanging the roles of F and G*)
-Goal "[| F : ensures A B;  G : stable A |] ==> F Join G : ensures A B";
+Goal "[| F : ensures A B;  G : stable A;  \
+\        States F = States G |] ==> F Join G : ensures A B";
 by (stac Join_commute 1);
+by (dtac sym 1);
 by (blast_tac (claset() addIs [ensures_stable_Join1]) 1);
 qed "ensures_stable_Join2";
 
 
 (** Diff and localTo **)
 
-Goalw [Join_def, Diff_def] "F Join (Diff G (Acts F)) = F Join G";
+
+Goal "States (Diff F acts) = States F";
+by (simp_tac (simpset() addsimps [Diff_def]) 1);
+qed "States_Diff";
+
+Goal "Init (Diff F acts) = Init F";
+by (auto_tac (claset() addIs [impOfSubs Init_subset_States],
+	      simpset() addsimps [Diff_def]));
+qed "Init_Diff";
+
+Goal "Acts (Diff F acts) = insert (diag (States F)) (Acts F - acts)";
+by (subgoal_tac "Acts F - acts <= Pow (States F Times States F)" 1);
+by (blast_tac (claset() addEs [equalityE] 
+                        addDs [impOfSubs Acts_subset_Pow_States]) 2);
+by (auto_tac (claset(), simpset() addsimps [Diff_def]));
+qed "Acts_Diff";
+
+Addsimps [States_Diff, Init_Diff, Acts_Diff];
+
+
+Goalw [Join_def] "States F = States G ==> F Join (Diff G (Acts F)) = F Join G";
 by (rtac program_equalityI 1);
-by Auto_tac;
+by (auto_tac (claset(), simpset() addsimps [insert_absorb]));
 qed "Join_Diff2";
 
-Goalw [Diff_def, Disjoint_def] "Disjoint F (Diff G (Acts F))";
+Goalw [Disjoint_def] "States F = States G ==> Disjoint F (Diff G (Acts F))";
 by Auto_tac;
 qed "Diff_Disjoint";
 
+Goalw [Disjoint_def] "Disjoint F G ==> States F = States G";
+by Auto_tac;
+qed "Disjoint_States_eq";
+
 Goal "[| F Join G : v localTo F;  Disjoint F G |] \
 \     ==> G : (INT z. stable {s. v s = z})";
 by (asm_full_simp_tac 
-    (simpset() addsimps [localTo_def, Diff_def, Disjoint_def,
+    (simpset() addsimps [localTo_def, Disjoint_def,
 			 Acts_Join, stable_def, constrains_def]) 1);
 by (Blast_tac 1);
 qed "localTo_imp_stable";
 
 Goal "[| F Join G : v localTo F;  (s,s') : act;  \
-\        act : Acts G;  Disjoint F G |] ==> v s' = v s";
+\        act : Acts G;  Disjoint F G  |] ==> v s' = v s";
 by (asm_full_simp_tac 
-    (simpset() addsimps [localTo_def, Diff_def, Disjoint_def,
+    (simpset() addsimps [localTo_def, Disjoint_def,
 			 Acts_Join, stable_def, constrains_def]) 1);
 by (Blast_tac 1);
 qed "localTo_imp_equals";
@@ -284,9 +433,15 @@
 \        F Join G : w localTo F;       \
 \        Disjoint F G |]               \
 \     ==> F Join G : constrains {s. P (v s) (w s)} {s. P' (v s) (w s)}";
-by (auto_tac (claset(), simpset() addsimps [constrains_def, Acts_Join]));
+by (auto_tac (claset(), 
+	      simpset() addsimps [constrains_def, 
+				  Disjoint_States_eq RS Acts_Join]));
 by (REPEAT_FIRST (dtac localTo_imp_equals THEN' REPEAT1 o atac));
-by Auto_tac;
+by (subgoal_tac "xa : States F" 1);
+by (force_tac
+    (claset() addSDs [Disjoint_States_eq,impOfSubs Acts_subset_Pow_States], 
+     simpset()) 2);
+by (Force_tac 1);
 qed "constrains_localTo_constrains2";
 
 Goalw [stable_def]
@@ -316,7 +471,8 @@
 by (rtac ballI 1);
 by (subgoal_tac "F Join G : constrains ({s. v s = k} Int {s. v s <= w s}) \
 \                                      ({s. v s = k} Un {s. v s <= w s})" 1);
-by (asm_simp_tac (simpset() addsimps [constrains_Join]) 2);
+by (asm_simp_tac
+    (simpset() addsimps [Disjoint_States_eq RS constrains_Join]) 2);
 by (blast_tac (claset() addIs [constrains_weaken]) 2);
 by (dtac (constrains_imp_Constrains RS Constrains_Int) 1 THEN etac INT_D 1);
 by (etac Constrains_weaken 2);
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/Union.thy
--- a/src/HOL/UNITY/Union.thy	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/Union.thy	Thu Dec 03 10:45:06 1998 +0100
@@ -11,25 +11,33 @@
 Union = SubstAx + FP +
 
 constdefs
+  eqStates :: ['a set, 'a => 'b program] => bool
+    "eqStates I F == EX St. ALL i:I. States (F i) = St"
+
   JOIN  :: ['a set, 'a => 'b program] => 'b program
-    "JOIN I F == mk_program (INT i:I. Init (F i), UN i:I. Acts (F i))"
+    "JOIN I F == mk_program (INT i:I. States (F i),
+			     INT i:I. Init (F i),
+			     UN i:I. Acts (F i))"
 
   Join :: ['a program, 'a program] => 'a program      (infixl 65)
-    "F Join G == mk_program (Init F Int Init G, Acts F Un Acts G)"
+    "F Join G == mk_program (States F Int States G,
+			     Init F Int Init G,
+			     Acts F Un Acts G)"
 
-  SKIP :: 'a program
-    "SKIP == mk_program (UNIV, {})"
+  SKIP :: 'a set => 'a program
+    "SKIP states == mk_program (states, states, {})"
 
   Diff :: "['a program, ('a * 'a)set set] => 'a program"
-    "Diff F acts == mk_program (Init F, Acts F - acts)"
+    "Diff F acts == mk_program (States F, Init F, Acts F - acts)"
 
   (*The set of systems that regard "v" as local to F*)
   localTo :: ['a => 'b, 'a program] => 'a program set  (infixl 80)
     "v localTo F == {G. ALL z. Diff G (Acts F) : stable {s. v s = z}}"
 
-  (*Two programs with disjoint actions, except for Id (idling)*)
+  (*Two programs with disjoint actions, except for identity actions *)
   Disjoint :: ['a program, 'a program] => bool
-    "Disjoint F G == Acts F Int Acts G <= {Id}"
+    "Disjoint F G == States F = States G &
+                     Acts F Int Acts G <= {diag (States G)}"
 
 syntax
   "@JOIN"      :: [pttrn, 'a set, 'b set] => 'b set  ("(3JN _:_./ _)" 10)
diff -r c48050d6928d -r 1894bfc4aee9 src/HOL/UNITY/WFair.ML
--- a/src/HOL/UNITY/WFair.ML	Wed Dec 02 16:14:09 1998 +0100
+++ b/src/HOL/UNITY/WFair.ML	Thu Dec 03 10:45:06 1998 +0100
@@ -8,6 +8,10 @@
 From Misra, "A Logic for Concurrent Programming", 1994
 *)
 
+    Goal "[| x:A;  P(x) |] ==> ? x:A. P(x)";
+    by (Blast_tac 1);
+    qed "rev_bexI";
+
 
 overload_1st_set "WFair.transient";
 overload_1st_set "WFair.ensures";
@@ -23,8 +27,7 @@
 Goalw [transient_def]
     "[| F : transient A; B<=A |] ==> F : transient B";
 by (Clarify_tac 1);
-by (rtac bexI 1 THEN assume_tac 2);
-by (Blast_tac 1);
+by (blast_tac (claset() addSIs [rev_bexI]) 1);
 qed "transient_strengthen";
 
 Goalw [transient_def]