# HG changeset patch
# User paulson
# Date 902307445 -7200
# Node ID 82a5ca6290aa37a192b2bb98ee821c1d91244ed0
# Parent  1b0f14d111429d02b7a481fb90c0dd7aafd34185
New record type of programs

diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/Channel.ML
--- a/src/HOL/UNITY/Channel.ML	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Channel.ML	Wed Aug 05 10:57:25 1998 +0200
@@ -26,8 +26,7 @@
 by (Blast_tac 1);
 qed_spec_mp "minSet_nonempty";
 
-Goal
-    "leadsTo Acts (minSet -`` {Some x}) (minSet -`` (Some``greaterThan x))";
+Goal "leadsTo acts (minSet -`` {Some x}) (minSet -`` (Some``greaterThan x))";
 by (rtac leadsTo_weaken 1);
 by (rtac ([UC2, UC1] MRS PSP) 1);
 by (ALLGOALS Asm_simp_tac);
@@ -39,7 +38,7 @@
 
 
 (*The induction*)
-Goal "leadsTo Acts (UNIV-{{}}) (minSet -`` (Some``atLeast y))";
+Goal "leadsTo acts (UNIV-{{}}) (minSet -`` (Some``atLeast y))";
 by (rtac leadsTo_weaken_R 1);
 by (res_inst_tac  [("l", "y"), ("f", "the o minSet"), ("B", "{}")]
      greaterThan_bounded_induct 1);
@@ -55,7 +54,7 @@
 val lemma = result();
 
 
-Goal "!!y::nat. leadsTo Acts (UNIV-{{}}) {s. y ~: s}";
+Goal "!!y::nat. leadsTo acts (UNIV-{{}}) {s. y ~: s}";
 by (rtac (lemma RS leadsTo_weaken_R) 1);
 by (Clarify_tac 1);
 by (forward_tac [minSet_nonempty] 1);
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/Channel.thy
--- a/src/HOL/UNITY/Channel.thy	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Channel.thy	Wed Aug 05 10:57:25 1998 +0200
@@ -18,12 +18,12 @@
 
 rules
 
-  skip "id: Acts"
+  skip "id: acts"
 
-  UC1  "constrains Acts (minSet -`` {Some x}) (minSet -`` (Some``atLeast x))"
+  UC1  "constrains acts (minSet -`` {Some x}) (minSet -`` (Some``atLeast x))"
 
-  (*  UC1  "constrains Acts {s. minSet s = x} {s. x <= minSet s}"  *)
+  (*  UC1  "constrains acts {s. minSet s = x} {s. x <= minSet s}"  *)
 
-  UC2  "leadsTo Acts (minSet -`` {Some x}) {s. x ~: s}"
+  UC2  "leadsTo acts (minSet -`` {Some x}) {s. x ~: s}"
 
 end
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/Common.ML
--- a/src/HOL/UNITY/Common.ML	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Common.ML	Wed Aug 05 10:57:25 1998 +0200
@@ -10,12 +10,9 @@
 From Misra, "A Logic for Concurrent Programming" (1994), sections 5.1 and 13.1.
 *)
 
-
-open Common;
-
 (*Misra's property CMT4: t exceeds no common meeting time*)
-Goal "[| ALL m. constrains Acts {m} (maxfg m); n: common |] \
-\     ==> stable Acts (atMost n)";
+Goal "[| ALL m. constrains acts {m} (maxfg m); n: common |] \
+\     ==> stable acts (atMost n)";
 by (dres_inst_tac [("P", "%t. t<=n")] elimination_sing 1);
 by (asm_full_simp_tac
     (simpset() addsimps [atMost_def, stable_def, common_def, maxfg_def,
@@ -27,8 +24,8 @@
 			addIs [order_eq_refl, fmono, gmono, le_trans]) 1);
 qed "common_stable";
 
-Goal "[| ALL m. constrains Acts {m} (maxfg m); n: common |] \
-\     ==> invariant ({0},Acts) (atMost n)";
+Goal "[| ALL m. constrains acts {m} (maxfg m); n: common |] \
+\     ==> invariant (|Init={0}, Acts=acts|) (atMost n)";
 by (rtac invariantI 1);
 by (asm_simp_tac (simpset() addsimps [common_stable]) 2);
 by (simp_tac (simpset() addsimps [atMost_def]) 1);
@@ -75,10 +72,10 @@
 Addsimps [atMost_Int_atLeast];
 
 Goal
-    "[| ALL m. constrains Acts {m} (maxfg m); \
-\               ALL m: lessThan n. leadsTo Acts {m} (greaterThan m); \
-\               n: common;  id: Acts |]  \
-\            ==> leadsTo Acts (atMost n) common";
+    "[| ALL m. constrains acts {m} (maxfg m); \
+\               ALL m: lessThan n. leadsTo acts {m} (greaterThan m); \
+\               n: common;  id: acts |]  \
+\            ==> leadsTo acts (atMost n) common";
 by (rtac leadsTo_weaken_R 1);
 by (res_inst_tac [("f","%x. x"), ("l", "n")] greaterThan_bounded_induct 1);
 by (ALLGOALS Asm_simp_tac);
@@ -89,10 +86,10 @@
 
 (*The "ALL m: Compl common" form echoes CMT6.*)
 Goal
-    "[| ALL m. constrains Acts {m} (maxfg m); \
-\               ALL m: Compl common. leadsTo Acts {m} (greaterThan m); \
-\               n: common;  id: Acts |]  \
-\            ==> leadsTo Acts (atMost (LEAST n. n: common)) common";
+    "[| ALL m. constrains acts {m} (maxfg m); \
+\               ALL m: Compl common. leadsTo acts {m} (greaterThan m); \
+\               n: common;  id: acts |]  \
+\            ==> leadsTo acts (atMost (LEAST n. n: common)) common";
 by (rtac lemma 1);
 by (ALLGOALS Asm_simp_tac);
 by (etac LeastI 2);
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/Mutex.ML
--- a/src/HOL/UNITY/Mutex.ML	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Mutex.ML	Wed Aug 05 10:57:25 1998 +0200
@@ -9,14 +9,14 @@
 (*split_all_tac causes a big blow-up*)
 claset_ref() := claset() delSWrapper "split_all_tac";
 
-val cmd_defs = [mutex_def, 
+val cmd_defs = [Mprg_def, 
 		cmd0U_def, cmd1U_def, cmd2U_def, cmd3U_def, cmd4U_def, 
 		cmd0V_def, cmd1V_def, cmd2V_def, cmd3V_def, cmd4V_def];
 
-Goalw [mutex_def] "id : mutex";
+Goalw [Mprg_def] "id : Acts Mprg";
 by (Simp_tac 1);
-qed "id_in_mutex";
-AddIffs [id_in_mutex];
+qed "id_in_Acts";
+AddIffs [id_in_Acts];
 
 
 (*Simplification for records*)
@@ -30,30 +30,30 @@
 Addsimps [invariantU_def, invariantV_def];
 
 
-Goalw [MInit_def] "invariant (MInit,mutex) invariantU";
+Goalw [Mprg_def] "invariant Mprg invariantU";
 by (rtac invariantI 1);
 by (constrains_tac cmd_defs 2);
 by Auto_tac;
 qed "invariantU";
 
-Goalw [MInit_def] "invariant (MInit,mutex) invariantV";
+Goalw [Mprg_def] "invariant Mprg invariantV";
 by (rtac invariantI 1);
 by (constrains_tac cmd_defs 2);
 by Auto_tac;
 qed "invariantV";
 
-val mutex_invariant = invariant_Int_rule [invariantU, invariantV];
+val invariantUV = invariant_Int_rule [invariantU, invariantV];
 
 
 (*The safety property: mutual exclusion*)
-Goal "disjoint (reachable (MInit,mutex)) {s. MM s = 3 & NN s = 3}";
-by (cut_facts_tac [mutex_invariant RS invariant_includes_reachable] 1);
+Goal "(reachable Mprg) Int {s. MM s = 3 & NN s = 3} = {}";
+by (cut_facts_tac [invariantUV RS invariant_includes_reachable] 1);
 by Auto_tac;
 qed "mutual_exclusion";
 
 
 (*The bad invariant FAILS in cmd1V*)
-Goalw [bad_invariantU_def] "stable mutex bad_invariantU";
+Goalw [bad_invariantU_def] "stable (Acts Mprg) bad_invariantU";
 by (constrains_tac cmd_defs 1);
 by (REPEAT (trans_tac 1));
 by (safe_tac (claset() addSEs [le_SucE]));
@@ -67,49 +67,48 @@
 
 (*** Progress for U ***)
 
-Goalw [unless_def] "unless mutex {s. MM s=2} {s. MM s=3}";
+Goalw [unless_def] "unless (Acts Mprg) {s. MM s=2} {s. MM s=3}";
 by (constrains_tac cmd_defs 1);
 qed "U_F0";
 
-Goal "LeadsTo(MInit,mutex) {s. MM s=1} {s. PP s = VV s & MM s = 2}";
+Goal "LeadsTo Mprg {s. MM s=1} {s. PP s = VV s & MM s = 2}";
 by (ensures_tac cmd_defs "cmd1U" 1);
 qed "U_F1";
 
-Goal "LeadsTo(MInit,mutex) {s. ~ PP s & MM s = 2} {s. MM s = 3}";
-by (cut_facts_tac [mutex_invariant] 1);
+Goal "LeadsTo Mprg {s. ~ PP s & MM s = 2} {s. MM s = 3}";
+by (cut_facts_tac [invariantUV] 1);
+bw Mprg_def;
 by (ensures_tac cmd_defs "cmd2U" 1);
 qed "U_F2";
 
-Goalw [mutex_def] "LeadsTo(MInit,mutex) {s. MM s = 3} {s. PP s}";
+Goal "LeadsTo Mprg {s. MM s = 3} {s. PP s}";
 by (rtac leadsTo_imp_LeadsTo 1); 
 by (res_inst_tac [("B", "{s. MM s = 4}")] leadsTo_Trans 1);
 by (ensures_tac cmd_defs "cmd4U" 2);
 by (ensures_tac cmd_defs "cmd3U" 1);
 qed "U_F3";
 
-Goal "LeadsTo(MInit,mutex) {s. MM s = 2} {s. PP s}";
+Goal "LeadsTo Mprg {s. MM s = 2} {s. PP s}";
 by (rtac ([LeadsTo_weaken_L, subset_refl RS subset_imp_LeadsTo] 
 	  MRS LeadsTo_Diff) 1);
 by (rtac ([U_F2, U_F3] MRS LeadsTo_Trans) 1);
 by (auto_tac (claset() addSEs [less_SucE], simpset()));
 val U_lemma2 = result();
 
-Goal "LeadsTo(MInit,mutex) {s. MM s = 1} {s. PP s}";
+Goal "LeadsTo Mprg {s. MM s = 1} {s. PP s}";
 by (rtac ([U_F1 RS LeadsTo_weaken_R, U_lemma2] MRS LeadsTo_Trans) 1);
 by (Blast_tac 1);
 val U_lemma1 = result();
 
-
-Goal "LeadsTo(MInit,mutex) {s. 1 <= MM s & MM s <= 3} {s. PP s}";
+Goal "LeadsTo Mprg {s. 1 <= MM s & MM s <= 3} {s. PP s}";
 by (simp_tac (simpset() addsimps [le_Suc_eq, conj_disj_distribL] 
 	                addcongs [rev_conj_cong]) 1);
 by (simp_tac (simpset() addsimps [Collect_disj_eq, LeadsTo_Un_distrib,
 				  U_lemma1, U_lemma2, U_F3] ) 1);
 val U_lemma123 = result();
 
-
 (*Misra's F4*)
-Goal "LeadsTo(MInit,mutex) {s. UU s} {s. PP s}";
+Goal "LeadsTo Mprg {s. UU s} {s. PP s}";
 by (rtac ([invariantU, U_lemma123] MRS invariant_LeadsTo_weaken) 1);
 by Auto_tac;
 qed "u_leadsto_p";
@@ -118,39 +117,39 @@
 (*** Progress for V ***)
 
 
-Goalw [unless_def] "unless mutex {s. NN s=2} {s. NN s=3}";
+Goalw [unless_def] "unless (Acts Mprg) {s. NN s=2} {s. NN s=3}";
 by (constrains_tac cmd_defs 1);
 qed "V_F0";
 
-Goal "LeadsTo(MInit,mutex) {s. NN s=1} {s. PP s = (~ UU s) & NN s = 2}";
+Goal "LeadsTo Mprg {s. NN s=1} {s. PP s = (~ UU s) & NN s = 2}";
 by (ensures_tac cmd_defs "cmd1V" 1);
 qed "V_F1";
 
-Goal "LeadsTo(MInit,mutex) {s. PP s & NN s = 2} {s. NN s = 3}";
-by (cut_facts_tac [mutex_invariant] 1);
+Goal "LeadsTo Mprg {s. PP s & NN s = 2} {s. NN s = 3}";
+by (cut_facts_tac [invariantUV] 1);
 by (ensures_tac cmd_defs "cmd2V" 1);
 qed "V_F2";
 
-Goalw [mutex_def] "LeadsTo(MInit,mutex) {s. NN s = 3} {s. ~ PP s}";
+Goal "LeadsTo Mprg {s. NN s = 3} {s. ~ PP s}";
 by (rtac leadsTo_imp_LeadsTo 1); 
 by (res_inst_tac [("B", "{s. NN s = 4}")] leadsTo_Trans 1);
 by (ensures_tac cmd_defs "cmd4V" 2);
 by (ensures_tac cmd_defs "cmd3V" 1);
 qed "V_F3";
 
-Goal "LeadsTo(MInit,mutex) {s. NN s = 2} {s. ~ PP s}";
+Goal "LeadsTo Mprg {s. NN s = 2} {s. ~ PP s}";
 by (rtac ([LeadsTo_weaken_L, subset_refl RS subset_imp_LeadsTo] 
 	  MRS LeadsTo_Diff) 1);
 by (rtac ([V_F2, V_F3] MRS LeadsTo_Trans) 1);
 by (auto_tac (claset() addSEs [less_SucE], simpset()));
 val V_lemma2 = result();
 
-Goal "LeadsTo(MInit,mutex) {s. NN s = 1} {s. ~ PP s}";
+Goal "LeadsTo Mprg {s. NN s = 1} {s. ~ PP s}";
 by (rtac ([V_F1 RS LeadsTo_weaken_R, V_lemma2] MRS LeadsTo_Trans) 1);
 by (Blast_tac 1);
 val V_lemma1 = result();
 
-Goal "LeadsTo(MInit,mutex) {s. 1 <= NN s & NN s <= 3} {s. ~ PP s}";
+Goal "LeadsTo Mprg {s. 1 <= NN s & NN s <= 3} {s. ~ PP s}";
 by (simp_tac (simpset() addsimps [le_Suc_eq, conj_disj_distribL] 
 	                addcongs [rev_conj_cong]) 1);
 by (simp_tac (simpset() addsimps [Collect_disj_eq, LeadsTo_Un_distrib,
@@ -159,7 +158,7 @@
 
 
 (*Misra's F4*)
-Goal "LeadsTo(MInit,mutex) {s. VV s} {s. ~ PP s}";
+Goal "LeadsTo Mprg {s. VV s} {s. ~ PP s}";
 by (rtac ([invariantV, V_lemma123] MRS invariant_LeadsTo_weaken) 1);
 by Auto_tac;
 qed "v_leadsto_not_p";
@@ -168,7 +167,7 @@
 (** Absence of starvation **)
 
 (*Misra's F6*)
-Goal "LeadsTo(MInit,mutex) {s. MM s = 1} {s. MM s = 3}";
+Goal "LeadsTo Mprg {s. MM s = 1} {s. MM s = 3}";
 by (rtac LeadsTo_Un_duplicate 1);
 by (rtac LeadsTo_cancel2 1);
 by (rtac U_F2 2);
@@ -182,7 +181,7 @@
 
 
 (*The same for V*)
-Goal "LeadsTo(MInit,mutex) {s. NN s = 1} {s. NN s = 3}";
+Goal "LeadsTo Mprg {s. NN s = 1} {s. NN s = 3}";
 by (rtac LeadsTo_Un_duplicate 1);
 by (rtac LeadsTo_cancel2 1);
 by (rtac V_F2 2);
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/Mutex.thy
--- a/src/HOL/UNITY/Mutex.thy	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Mutex.thy	Wed Aug 05 10:57:25 1998 +0200
@@ -26,6 +26,9 @@
   VV :: bool
 
 constdefs
+  
+  (** The program for process U **)
+  
   cmd0U :: "(state*state) set"
     "cmd0U == {(s,s'). s' = s (|UU:=True, MM:=1|) & MM s = 0}"
 
@@ -41,6 +44,8 @@
   cmd4U :: "(state*state) set"
     "cmd4U == {(s,s'). s' = s (|PP:=True, MM:=0|) & MM s = 4}"
 
+  (** The program for process V **)
+  
   cmd0V :: "(state*state) set"
     "cmd0V == {(s,s'). s' = s (|VV:=True, NN:=1|) & NN s = 0}"
 
@@ -56,10 +61,12 @@
   cmd4V :: "(state*state) set"
     "cmd4V == {(s,s'). s' = s (|PP:=False, NN:=0|) & NN s = 4}"
 
-  mutex :: "(state*state) set set"
-    "mutex == {id,
-	       cmd0U, cmd1U, cmd2U, cmd3U, cmd4U, 
-	       cmd0V, cmd1V, cmd2V, cmd3V, cmd4V}"
+  Mprg :: state program
+    "Mprg == (|Init = {s. ~ UU s & ~ VV s & MM s = 0 & NN s = 0},
+	       Acts = {id,
+	               cmd0U, cmd1U, cmd2U, cmd3U, cmd4U, 
+	               cmd0V, cmd1V, cmd2V, cmd3V, cmd4V}|)"
+
 
   (** The correct invariants **)
 
@@ -77,7 +84,4 @@
     "bad_invariantU == {s. (UU s = (1 <= MM s & MM s <= 3)) &
 		           (3 <= MM s & MM s <= 4 --> ~ PP s)}"
 
-  MInit :: "state set"
-    "MInit == {s. ~ UU s & ~ VV s & MM s = 0 & NN s = 0}"
-
 end
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/ROOT.ML
--- a/src/HOL/UNITY/ROOT.ML	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/ROOT.ML	Wed Aug 05 10:57:25 1998 +0200
@@ -19,3 +19,4 @@
 time_use_thy "Mutex";
 time_use_thy "FP";
 time_use_thy "Reach";
+time_use_thy "Handshake";
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/Reach.ML
--- a/src/HOL/UNITY/Reach.ML	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Reach.ML	Wed Aug 05 10:57:25 1998 +0200
@@ -19,22 +19,22 @@
 AddSEs [ifE];
 
 
-val cmd_defs = [racts_def, asgt_def, fun_upd_def];
+val cmd_defs = [Rprg_def, asgt_def, fun_upd_def];
 
-Goalw [racts_def] "id : racts";
+Goalw [Rprg_def] "id : (Acts Rprg)";
 by (Simp_tac 1);
-qed "id_in_racts";
-AddIffs [id_in_racts];
+qed "id_in_Acts";
+AddIffs [id_in_Acts];
 
 (*All vertex sets are finite*)
 AddIffs [[subset_UNIV, finite_graph] MRS finite_subset];
 
 Addsimps [reach_invariant_def];
 
-Goalw [rinit_def] "invariant (rinit,racts) reach_invariant";
+Goalw [Rprg_def] "invariant Rprg reach_invariant";
 by (rtac invariantI 1);
 by Auto_tac;  (*for the initial state; proof of stability remains*)
-by (constrains_tac [racts_def, asgt_def] 1);
+by (constrains_tac [Rprg_def, asgt_def] 1);
 by (blast_tac (claset() addIs [r_into_rtrancl,rtrancl_trans]) 1);
 qed "reach_invariant";
 
@@ -52,7 +52,7 @@
 qed "fixedpoint_invariant_correct";
 
 Goalw (cmd_defs @ [FP_def, fixedpoint_def, stable_def, constrains_def])
-    "FP racts <= fixedpoint";
+    "FP (Acts Rprg) <= fixedpoint";
 by Auto_tac;
 by (dtac bspec 1); 
 by (Blast_tac 1);
@@ -62,11 +62,11 @@
 val lemma1 = result();
 
 Goalw (cmd_defs @ [FP_def, fixedpoint_def, stable_def, constrains_def])
-    "fixedpoint <= FP racts";
+    "fixedpoint <= FP (Acts Rprg)";
 by (auto_tac (claset() addIs [ext], simpset()));
 val lemma2 = result();
 
-Goal "FP racts = fixedpoint";
+Goal "FP (Acts Rprg) = fixedpoint";
 by (rtac ([lemma1,lemma2] MRS equalityI) 1);
 qed "FP_fixedpoint";
 
@@ -80,7 +80,7 @@
 Goal "Compl fixedpoint = (UN (u,v): edges. {s. s u & ~ s v})";
 by (simp_tac (simpset() addsimps
 	      ([Compl_FP, UN_UN_flatten, FP_fixedpoint RS sym, 
-		racts_def, asgt_def])) 1);
+		Rprg_def, asgt_def])) 1);
 by Safe_tac;
 by (rtac fun_upd_idem 1);
 by (Blast_tac 1);
@@ -118,34 +118,34 @@
 qed "metric_le";
 
 Goal "(u,v): edges ==> \
-\              ensures racts ((metric-``{m}) Int {s. s u & ~ s v})  \
+\              ensures (Acts Rprg) ((metric-``{m}) Int {s. s u & ~ s v})  \
 \                            (metric-``(lessThan m))";
-by (ensures_tac [racts_def, asgt_def] "asgt u v" 1);
+by (ensures_tac [Rprg_def, asgt_def] "asgt u v" 1);
 by (cut_facts_tac [metric_le] 1);
 by (fast_tac (claset() addSDs [le_imp_less_or_eq]) 1);
 qed "edges_ensures";
 
-Goal "leadsTo racts ((metric-``{m}) - fixedpoint) (metric-``(lessThan m))";
+Goal "leadsTo (Acts Rprg) ((metric-``{m}) - fixedpoint) (metric-``(lessThan m))";
 by (simp_tac (simpset() addsimps [Diff_fixedpoint]) 1);
 by (rtac leadsTo_UN 1);
 by (split_all_tac 1);
 by (asm_simp_tac (simpset() addsimps [edges_ensures RS leadsTo_Basis]) 1);
 qed "leadsTo_Diff_fixedpoint";
 
-Goal "leadsTo racts (metric-``{m}) (metric-``(lessThan m) Un fixedpoint)";
+Goal "leadsTo (Acts Rprg) (metric-``{m}) (metric-``(lessThan m) Un fixedpoint)";
 by (rtac (leadsTo_Diff_fixedpoint RS leadsTo_weaken_R RS leadsTo_Diff) 1);
 by (ALLGOALS (blast_tac (claset() addIs [subset_imp_leadsTo])));
 qed "leadsTo_Un_fixedpoint";
 
 
 (*Execution in any state leads to a fixedpoint (i.e. can terminate)*)
-Goal "leadsTo racts UNIV fixedpoint";
+Goal "leadsTo (Acts Rprg) UNIV fixedpoint";
 by (rtac lessThan_induct 1);
 by Auto_tac;
 by (rtac leadsTo_Un_fixedpoint 1);
 qed "leadsTo_fixedpoint";
 
-Goal "LeadsTo(rinit,racts) UNIV { %v. (init, v) : edges^* }";
+Goal "LeadsTo Rprg UNIV { %v. (init, v) : edges^* }";
 by (stac (fixedpoint_invariant_correct RS sym) 1);
 by (rtac ([reach_invariant,
 	   leadsTo_fixedpoint RS leadsTo_imp_LeadsTo] 
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/Reach.thy
--- a/src/HOL/UNITY/Reach.thy	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Reach.thy	Wed Aug 05 10:57:25 1998 +0200
@@ -23,11 +23,9 @@
   asgt  :: "[vertex,vertex] => (state*state) set"
     "asgt u v == {(s,s'). s' = s(v:= s u | s v)}"
 
-  racts :: "(state*state) set set"
-    "racts == insert id (UN (u,v): edges. {asgt u v})"
-
-  rinit :: "state set"
-    "rinit == {%v. v=init}"
+  Rprg :: state program
+    "Rprg == (|Init = {%v. v=init},
+	       Acts = insert id (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 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/SubstAx.ML
--- a/src/HOL/UNITY/SubstAx.ML	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/SubstAx.ML	Wed Aug 05 10:57:25 1998 +0200
@@ -16,31 +16,27 @@
 
 (*** Introduction rules: Basis, Trans, Union ***)
 
-Goal "leadsTo Acts A B ==> LeadsTo(Init,Acts) A B";
+Goal "leadsTo (Acts prg) A B ==> LeadsTo prg A B";
 by (simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (blast_tac (claset() addIs [PSP_stable2, stable_reachable]) 1);
 qed "leadsTo_imp_LeadsTo";
 
-Goal "[| constrains Acts (reachable(Init,Acts) Int (A - A'))   \
-\                         (A Un A'); \
-\         transient  Acts (reachable(Init,Acts) Int (A-A')) |]   \
-\     ==> LeadsTo(Init,Acts) A A'";
-by (simp_tac (simpset() addsimps [LeadsTo_def]) 1);
+Goal "ensures (Acts prg) (reachable prg Int A) (reachable prg Int A') \
+\     ==> LeadsTo prg A A'";
+by (full_simp_tac (simpset() addsimps [ensures_def, LeadsTo_def]) 1);
 by (rtac (stable_reachable RS stable_ensures_Int RS leadsTo_Basis) 1);
-by (assume_tac 2);
-by (asm_simp_tac 
-    (simpset() addsimps [Int_Un_distrib RS sym, Diff_Int_distrib RS sym,
-			 stable_constrains_Int]) 1);
+by (ALLGOALS (asm_full_simp_tac (simpset() addsimps [Diff_Int_distrib])));
+by (blast_tac (claset() addIs [constrains_weaken]) 1);
 qed "LeadsTo_Basis";
 
-Goal "[| LeadsTo(Init,Acts) A B;  LeadsTo(Init,Acts) B C |] \
-\      ==> LeadsTo(Init,Acts) A C";
+Goal "[| LeadsTo prg A B;  LeadsTo prg B C |] \
+\      ==> LeadsTo prg A C";
 by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (blast_tac (claset() addIs [leadsTo_Trans]) 1);
 qed "LeadsTo_Trans";
 
 val [prem] = goalw thy [LeadsTo_def]
- "(!!A. A : S ==> LeadsTo(Init,Acts) A B) ==> LeadsTo(Init,Acts) (Union S) B";
+ "(!!A. A : S ==> LeadsTo prg A B) ==> LeadsTo prg (Union S) B";
 by (Simp_tac 1);
 by (stac Int_Union 1);
 by (blast_tac (claset() addIs [leadsTo_UN,
@@ -50,42 +46,42 @@
 
 (*** Derived rules ***)
 
-Goal "id: Acts ==> LeadsTo(Init,Acts) A UNIV";
+Goal "id: (Acts prg) ==> LeadsTo prg A UNIV";
 by (asm_simp_tac (simpset() addsimps [LeadsTo_def, 
 				      Int_lower1 RS subset_imp_leadsTo]) 1);
 qed "LeadsTo_UNIV";
 Addsimps [LeadsTo_UNIV];
 
 (*Useful with cancellation, disjunction*)
-Goal "LeadsTo(Init,Acts) A (A' Un A') ==> LeadsTo(Init,Acts) A A'";
+Goal "LeadsTo prg A (A' Un A') ==> LeadsTo prg A A'";
 by (asm_full_simp_tac (simpset() addsimps Un_ac) 1);
 qed "LeadsTo_Un_duplicate";
 
-Goal "LeadsTo(Init,Acts) A (A' Un C Un C) ==> LeadsTo(Init,Acts) A (A' Un C)";
+Goal "LeadsTo prg A (A' Un C Un C) ==> LeadsTo prg A (A' Un C)";
 by (asm_full_simp_tac (simpset() addsimps Un_ac) 1);
 qed "LeadsTo_Un_duplicate2";
 
 val prems = goal thy
-   "(!!i. i : I ==> LeadsTo(Init,Acts) (A i) B) \
-\   ==> LeadsTo(Init,Acts) (UN i:I. A i) B";
+   "(!!i. i : I ==> LeadsTo prg (A i) B) \
+\   ==> LeadsTo prg (UN i:I. A i) B";
 by (simp_tac (simpset() addsimps [Union_image_eq RS sym]) 1);
 by (blast_tac (claset() addIs (LeadsTo_Union::prems)) 1);
 qed "LeadsTo_UN";
 
 (*Binary union introduction rule*)
-Goal "[| LeadsTo(Init,Acts) A C; LeadsTo(Init,Acts) B C |] ==> LeadsTo(Init,Acts) (A Un B) C";
+Goal "[| LeadsTo prg A C; LeadsTo prg B C |] ==> LeadsTo prg (A Un B) C";
 by (stac Un_eq_Union 1);
 by (blast_tac (claset() addIs [LeadsTo_Union]) 1);
 qed "LeadsTo_Un";
 
 
-Goal "[| reachable(Init,Acts) Int A <= B;  id: Acts |] \
-\     ==> LeadsTo(Init,Acts) A B";
+Goal "[| reachable prg Int A <= B;  id: (Acts prg) |] \
+\     ==> LeadsTo prg A B";
 by (simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (blast_tac (claset() addIs [subset_imp_leadsTo]) 1);
 qed "Int_subset_imp_LeadsTo";
 
-Goal "[| A <= B;  id: Acts |] ==> LeadsTo(Init,Acts) A B";
+Goal "[| A <= B;  id: (Acts prg) |] ==> LeadsTo prg A B";
 by (simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (blast_tac (claset() addIs [subset_imp_leadsTo]) 1);
 qed "subset_imp_LeadsTo";
@@ -93,61 +89,62 @@
 bind_thm ("empty_LeadsTo", empty_subsetI RS subset_imp_LeadsTo);
 Addsimps [empty_LeadsTo];
 
-Goal "[| reachable(Init,Acts) Int A = {};  id: Acts |] \
-\     ==> LeadsTo(Init,Acts) A B";
+Goal "[| reachable prg Int A = {};  id: (Acts prg) |] \
+\     ==> LeadsTo prg A B";
 by (asm_simp_tac (simpset() addsimps [Int_subset_imp_LeadsTo]) 1);
 qed "Int_empty_LeadsTo";
 
 
-Goal "[| LeadsTo(Init,Acts) A A';   \
-\        reachable(Init,Acts) Int A' <= B' |] \
-\     ==> LeadsTo(Init,Acts) A B'";
+Goal "[| LeadsTo prg A A';   \
+\        reachable prg Int A' <= B' |] \
+\     ==> LeadsTo prg A B'";
 by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (blast_tac (claset() addIs [leadsTo_weaken_R]) 1);
 qed_spec_mp "LeadsTo_weaken_R";
 
 
-Goal "[| LeadsTo(Init,Acts) A A'; \
-\        reachable(Init,Acts) Int B <= A; id: Acts |]  \
-\     ==> LeadsTo(Init,Acts) B A'";
+Goal "[| LeadsTo prg A A'; \
+\        reachable prg Int B <= A; id: (Acts prg) |]  \
+\     ==> LeadsTo prg B A'";
 by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (blast_tac (claset() addIs [leadsTo_weaken_L]) 1);
 qed_spec_mp "LeadsTo_weaken_L";
 
 
 (*Distributes over binary unions*)
-Goal "id: Acts ==> \
-\       LeadsTo(Init,Acts) (A Un B) C  =  \
-\       (LeadsTo(Init,Acts) A C & LeadsTo(Init,Acts) B C)";
+Goal "id: (Acts prg) ==> \
+\       LeadsTo prg (A Un B) C  =  \
+\       (LeadsTo prg A C & LeadsTo prg B C)";
 by (blast_tac (claset() addIs [LeadsTo_Un, LeadsTo_weaken_L]) 1);
 qed "LeadsTo_Un_distrib";
 
-Goal "id: Acts ==> \
-\       LeadsTo(Init,Acts) (UN i:I. A i) B  =  \
-\       (ALL i : I. LeadsTo(Init,Acts) (A i) B)";
+Goal "id: (Acts prg) ==> \
+\       LeadsTo prg (UN i:I. A i) B  =  \
+\       (ALL i : I. LeadsTo prg (A i) B)";
 by (blast_tac (claset() addIs [LeadsTo_UN, LeadsTo_weaken_L]) 1);
 qed "LeadsTo_UN_distrib";
 
-Goal "id: Acts ==> \
-\       LeadsTo(Init,Acts) (Union S) B  =  \
-\       (ALL A : S. LeadsTo(Init,Acts) A B)";
+Goal "id: (Acts prg) ==> \
+\       LeadsTo prg (Union S) B  =  \
+\       (ALL A : S. LeadsTo prg A B)";
 by (blast_tac (claset() addIs [LeadsTo_Union, LeadsTo_weaken_L]) 1);
 qed "LeadsTo_Union_distrib";
 
 
-Goal "[| LeadsTo(Init,Acts) A A'; id: Acts;   \
-\        reachable(Init,Acts) Int B  <= A;     \
-\        reachable(Init,Acts) Int A' <= B' |] \
-\     ==> LeadsTo(Init,Acts) B B'";
+Goal "[| LeadsTo prg A A'; id: (Acts prg);   \
+\        reachable prg Int B  <= A;     \
+\        reachable prg Int A' <= B' |] \
+\     ==> LeadsTo prg B B'";
 (*PROOF FAILED: why?*)
 by (blast_tac (claset() addIs [LeadsTo_Trans, LeadsTo_weaken_R,
 			       LeadsTo_weaken_L]) 1);
 qed "LeadsTo_weaken";
 
 
-(*Set difference: maybe combine with leadsTo_weaken_L??*)
-Goal "[| LeadsTo(Init,Acts) (A-B) C; LeadsTo(Init,Acts) B C; id: Acts |] \
-\       ==> LeadsTo(Init,Acts) A C";
+(*Set difference: maybe combine with leadsTo_weaken_L??
+  This is the most useful form of the "disjunction" rule*)
+Goal "[| LeadsTo prg (A-B) C; LeadsTo prg B C; id: (Acts prg) |] \
+\       ==> LeadsTo prg A C";
 by (blast_tac (claset() addIs [LeadsTo_Un, LeadsTo_weaken]) 1);
 qed "LeadsTo_Diff";
 
@@ -156,8 +153,8 @@
     see ball_constrains_UN in UNITY.ML***)
 
 val prems = goal thy
-   "(!! i. i:I ==> LeadsTo(Init,Acts) (A i) (A' i)) \
-\   ==> LeadsTo(Init,Acts) (UN i:I. A i) (UN i:I. A' i)";
+   "(!! i. i:I ==> LeadsTo prg (A i) (A' i)) \
+\   ==> LeadsTo prg (UN i:I. A i) (UN i:I. A' i)";
 by (simp_tac (simpset() addsimps [Union_image_eq RS sym]) 1);
 by (blast_tac (claset() addIs [LeadsTo_Union, LeadsTo_weaken_R] 
                         addIs prems) 1);
@@ -166,22 +163,22 @@
 
 (*Version with no index set*)
 val prems = goal thy
-   "(!! i. LeadsTo(Init,Acts) (A i) (A' i)) \
-\   ==> LeadsTo(Init,Acts) (UN i. A i) (UN i. A' i)";
+   "(!! i. LeadsTo prg (A i) (A' i)) \
+\   ==> LeadsTo prg (UN i. A i) (UN i. A' i)";
 by (blast_tac (claset() addIs [LeadsTo_UN_UN] 
                         addIs prems) 1);
 qed "LeadsTo_UN_UN_noindex";
 
 (*Version with no index set*)
-Goal "ALL i. LeadsTo(Init,Acts) (A i) (A' i) \
-\           ==> LeadsTo(Init,Acts) (UN i. A i) (UN i. A' i)";
+Goal "ALL i. LeadsTo prg (A i) (A' i) \
+\           ==> LeadsTo prg (UN i. A i) (UN i. A' i)";
 by (blast_tac (claset() addIs [LeadsTo_UN_UN]) 1);
 qed "all_LeadsTo_UN_UN";
 
 
 (*Binary union version*)
-Goal "[| LeadsTo(Init,Acts) A A'; LeadsTo(Init,Acts) B B' |] \
-\                 ==> LeadsTo(Init,Acts) (A Un B) (A' Un B')";
+Goal "[| LeadsTo prg A A'; LeadsTo prg B B' |] \
+\                 ==> LeadsTo prg (A Un B) (A' Un B')";
 by (blast_tac (claset() addIs [LeadsTo_Un, 
 			       LeadsTo_weaken_R]) 1);
 qed "LeadsTo_Un_Un";
@@ -189,28 +186,28 @@
 
 (** The cancellation law **)
 
-Goal "[| LeadsTo(Init,Acts) A (A' Un B); LeadsTo(Init,Acts) B B'; \
-\              id: Acts |]    \
-\           ==> LeadsTo(Init,Acts) A (A' Un B')";
+Goal "[| LeadsTo prg A (A' Un B); LeadsTo prg B B'; \
+\              id: (Acts prg) |]    \
+\           ==> LeadsTo prg A (A' Un B')";
 by (blast_tac (claset() addIs [LeadsTo_Un_Un, 
 			       subset_imp_LeadsTo, LeadsTo_Trans]) 1);
 qed "LeadsTo_cancel2";
 
-Goal "[| LeadsTo(Init,Acts) A (A' Un B); LeadsTo(Init,Acts) (B-A') B'; id: Acts |] \
-\           ==> LeadsTo(Init,Acts) A (A' Un B')";
+Goal "[| LeadsTo prg A (A' Un B); LeadsTo prg (B-A') B'; id: (Acts prg) |] \
+\           ==> LeadsTo prg A (A' Un B')";
 by (rtac LeadsTo_cancel2 1);
 by (assume_tac 2);
 by (ALLGOALS Asm_simp_tac);
 qed "LeadsTo_cancel_Diff2";
 
-Goal "[| LeadsTo(Init,Acts) A (B Un A'); LeadsTo(Init,Acts) B B'; id: Acts |] \
-\           ==> LeadsTo(Init,Acts) A (B' Un A')";
+Goal "[| LeadsTo prg A (B Un A'); LeadsTo prg B B'; id: (Acts prg) |] \
+\           ==> LeadsTo prg A (B' Un A')";
 by (asm_full_simp_tac (simpset() addsimps [Un_commute]) 1);
 by (blast_tac (claset() addSIs [LeadsTo_cancel2]) 1);
 qed "LeadsTo_cancel1";
 
-Goal "[| LeadsTo(Init,Acts) A (B Un A'); LeadsTo(Init,Acts) (B-A') B'; id: Acts |] \
-\           ==> LeadsTo(Init,Acts) A (B' Un A')";
+Goal "[| LeadsTo prg A (B Un A'); LeadsTo prg (B-A') B'; id: (Acts prg) |] \
+\           ==> LeadsTo prg A (B' Un A')";
 by (rtac LeadsTo_cancel1 1);
 by (assume_tac 2);
 by (ALLGOALS Asm_simp_tac);
@@ -220,7 +217,7 @@
 
 (** The impossibility law **)
 
-Goal "LeadsTo(Init,Acts) A {} ==> reachable(Init,Acts) Int A  = {}";
+Goal "LeadsTo prg A {} ==> reachable prg Int A  = {}";
 by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (etac leadsTo_empty 1);
 qed "LeadsTo_empty";
@@ -229,20 +226,20 @@
 (** PSP: Progress-Safety-Progress **)
 
 (*Special case of PSP: Misra's "stable conjunction".  Doesn't need id:Acts. *)
-Goal "[| LeadsTo(Init,Acts) A A'; stable Acts B |] \
-\           ==> LeadsTo(Init,Acts) (A Int B) (A' Int B)";
+Goal "[| LeadsTo prg A A'; stable (Acts prg) B |] \
+\           ==> LeadsTo prg (A Int B) (A' Int B)";
 by (asm_full_simp_tac (simpset() addsimps [LeadsTo_def, Int_assoc RS sym, 
 					   PSP_stable]) 1);
 qed "R_PSP_stable";
 
-Goal "[| LeadsTo(Init,Acts) A A'; stable Acts B |] \
-\             ==> LeadsTo(Init,Acts) (B Int A) (B Int A')";
+Goal "[| LeadsTo prg A A'; stable (Acts prg) B |] \
+\             ==> LeadsTo prg (B Int A) (B Int A')";
 by (asm_simp_tac (simpset() addsimps (R_PSP_stable::Int_ac)) 1);
 qed "R_PSP_stable2";
 
 
-Goal "[| LeadsTo(Init,Acts) A A'; constrains Acts B B'; id: Acts |] \
-\           ==> LeadsTo(Init,Acts) (A Int B) ((A' Int B) Un (B' - B))";
+Goal "[| LeadsTo prg A A'; constrains (Acts prg) B B'; id: (Acts prg) |] \
+\           ==> LeadsTo prg (A Int B) ((A' Int B) Un (B' - B))";
 by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (dtac PSP 1);
 by (etac constrains_reachable 1);
@@ -250,14 +247,14 @@
 by (ALLGOALS Blast_tac);
 qed "R_PSP";
 
-Goal "[| LeadsTo(Init,Acts) A A'; constrains Acts B B'; id: Acts |] \
-\           ==> LeadsTo(Init,Acts) (B Int A) ((B Int A') Un (B' - B))";
+Goal "[| LeadsTo prg A A'; constrains (Acts prg) B B'; id: (Acts prg) |] \
+\           ==> LeadsTo prg (B Int A) ((B Int A') Un (B' - B))";
 by (asm_simp_tac (simpset() addsimps (R_PSP::Int_ac)) 1);
 qed "R_PSP2";
 
 Goalw [unless_def]
-   "[| LeadsTo(Init,Acts) A A'; unless Acts B B'; id: Acts |] \
-\           ==> LeadsTo(Init,Acts) (A Int B) ((A' Int B) Un B')";
+   "[| LeadsTo prg A A'; unless (Acts prg) B B'; id: (Acts prg) |] \
+\           ==> LeadsTo prg (A Int B) ((A' Int B) Un B')";
 by (dtac R_PSP 1);
 by (assume_tac 1);
 by (asm_full_simp_tac (simpset() addsimps [Un_Diff_Diff, Int_Diff_Un]) 2);
@@ -272,10 +269,10 @@
 
 (** Meta or object quantifier ????? **)
 Goal "[| wf r;     \
-\              ALL m. LeadsTo(Init,Acts) (A Int f-``{m})                     \
+\              ALL m. LeadsTo prg (A Int f-``{m})                     \
 \                                       ((A Int f-``(r^-1 ^^ {m})) Un B);   \
-\              id: Acts |] \
-\           ==> LeadsTo(Init,Acts) A B";
+\              id: (Acts prg) |] \
+\           ==> LeadsTo prg A B";
 by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (etac leadsTo_wf_induct 1);
 by (assume_tac 2);
@@ -284,10 +281,10 @@
 
 
 Goal "[| wf r;     \
-\        ALL m:I. LeadsTo(Init,Acts) (A Int f-``{m})                   \
+\        ALL m:I. LeadsTo prg (A Int f-``{m})                   \
 \                                    ((A Int f-``(r^-1 ^^ {m})) Un B);   \
-\        id: Acts |] \
-\     ==> LeadsTo(Init,Acts) A ((A - (f-``I)) Un B)";
+\        id: (Acts prg) |] \
+\     ==> LeadsTo prg A ((A - (f-``I)) Un B)";
 by (etac LeadsTo_wf_induct 1);
 by Safe_tac;
 by (case_tac "m:I" 1);
@@ -296,29 +293,29 @@
 qed "R_bounded_induct";
 
 
-Goal "[| ALL m. LeadsTo(Init,Acts) (A Int f-``{m})                     \
-\                                  ((A Int f-``(lessThan m)) Un B);   \
-\        id: Acts |] \
-\     ==> LeadsTo(Init,Acts) A B";
+Goal "[| ALL m. LeadsTo prg (A Int f-``{m})                     \
+\                           ((A Int f-``(lessThan m)) Un B);   \
+\        id: (Acts prg) |] \
+\     ==> LeadsTo prg A B";
 by (rtac (wf_less_than RS LeadsTo_wf_induct) 1);
 by (assume_tac 2);
 by (Asm_simp_tac 1);
 qed "R_lessThan_induct";
 
-Goal "[| ALL m:(greaterThan l). LeadsTo(Init,Acts) (A Int f-``{m})   \
+Goal "[| ALL m:(greaterThan l). LeadsTo prg (A Int f-``{m})   \
 \                                        ((A Int f-``(lessThan m)) Un B);   \
-\              id: Acts |] \
-\           ==> LeadsTo(Init,Acts) A ((A Int (f-``(atMost l))) Un B)";
+\              id: (Acts prg) |] \
+\           ==> LeadsTo prg A ((A Int (f-``(atMost l))) Un B)";
 by (simp_tac (HOL_ss addsimps [Diff_eq RS sym, vimage_Compl, Compl_greaterThan RS sym]) 1);
 by (rtac (wf_less_than RS R_bounded_induct) 1);
 by (assume_tac 2);
 by (Asm_simp_tac 1);
 qed "R_lessThan_bounded_induct";
 
-Goal "[| ALL m:(lessThan l). LeadsTo(Init,Acts) (A Int f-``{m})   \
+Goal "[| ALL m:(lessThan l). LeadsTo prg (A Int f-``{m})   \
 \                              ((A Int f-``(greaterThan m)) Un B);   \
-\        id: Acts |] \
-\     ==> LeadsTo(Init,Acts) A ((A Int (f-``(atLeast l))) Un B)";
+\        id: (Acts prg) |] \
+\     ==> LeadsTo prg A ((A Int (f-``(atLeast l))) Un B)";
 by (res_inst_tac [("f","f"),("f1", "%k. l - k")]
     (wf_less_than RS wf_inv_image RS LeadsTo_wf_induct) 1);
 by (assume_tac 2);
@@ -333,19 +330,19 @@
 
 (*** Completion: Binary and General Finite versions ***)
 
-Goal "[| LeadsTo(Init,Acts) A A';  stable Acts A';   \
-\        LeadsTo(Init,Acts) B B';  stable Acts B';  id: Acts |] \
-\     ==> LeadsTo(Init,Acts) (A Int B) (A' Int B')";
+Goal "[| LeadsTo prg A A';  stable (Acts prg) A';   \
+\        LeadsTo prg B B';  stable (Acts prg) B';  id: (Acts prg) |] \
+\     ==> LeadsTo prg (A Int B) (A' Int B')";
 by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (blast_tac (claset() addIs [stable_completion RS leadsTo_weaken] 
                         addSIs [stable_Int, stable_reachable]) 1);
 qed "R_stable_completion";
 
 
-Goal "[| finite I;  id: Acts |]                     \
-\     ==> (ALL i:I. LeadsTo(Init,Acts) (A i) (A' i)) -->  \
-\         (ALL i:I. stable Acts (A' i)) -->         \
-\         LeadsTo(Init,Acts) (INT i:I. A i) (INT i:I. A' i)";
+Goal "[| finite I;  id: (Acts prg) |]                     \
+\     ==> (ALL i:I. LeadsTo prg (A i) (A' i)) -->  \
+\         (ALL i:I. stable (Acts prg) (A' i)) -->         \
+\         LeadsTo prg (INT i:I. A i) (INT i:I. A' i)";
 by (etac finite_induct 1);
 by (Asm_simp_tac 1);
 by (asm_simp_tac 
@@ -354,10 +351,10 @@
 qed_spec_mp "R_finite_stable_completion";
 
 
-Goal "[| LeadsTo(Init,Acts) A (A' Un C);  constrains Acts A' (A' Un C); \
-\        LeadsTo(Init,Acts) B (B' Un C);  constrains Acts B' (B' Un C); \
-\        id: Acts |] \
-\     ==> LeadsTo(Init,Acts) (A Int B) ((A' Int B') Un C)";
+Goal "[| LeadsTo prg A (A' Un C);  constrains (Acts prg) A' (A' Un C); \
+\        LeadsTo prg B (B' Un C);  constrains (Acts prg) B' (B' Un C); \
+\        id: (Acts prg) |] \
+\     ==> LeadsTo prg (A Int B) ((A' Int B') Un C)";
 by (full_simp_tac (simpset() addsimps [LeadsTo_def, Int_Un_distrib]) 1);
 by (dtac completion 1);
 by (assume_tac 2);
@@ -368,10 +365,10 @@
 qed "R_completion";
 
 
-Goal "[| finite I;  id: Acts |] \
-\     ==> (ALL i:I. LeadsTo(Init,Acts) (A i) (A' i Un C)) -->  \
-\         (ALL i:I. constrains Acts (A' i) (A' i Un C)) --> \
-\         LeadsTo(Init,Acts) (INT i:I. A i) ((INT i:I. A' i) Un C)";
+Goal "[| finite I;  id: (Acts prg) |] \
+\     ==> (ALL i:I. LeadsTo prg (A i) (A' i Un C)) -->  \
+\         (ALL i:I. constrains (Acts prg) (A' i) (A' i Un C)) --> \
+\         LeadsTo prg (INT i:I. A i) ((INT i:I. A' i) Un C)";
 by (etac finite_induct 1);
 by (ALLGOALS Asm_simp_tac);
 by (Clarify_tac 1);
@@ -384,32 +381,37 @@
 (*** Specialized laws for handling invariants ***)
 
 Goalw [transient_def]
-    "[| reachable(Init,Acts) <= INV;  transient Acts (INV Int A) |]  \
-\    ==> transient Acts (reachable(Init,Acts) Int A)";
+    "[| reachable prg <= INV;  transient (Acts prg) (INV Int A) |]  \
+\    ==> transient (Acts prg) (reachable prg Int A)";
 by (Clarify_tac 1);
 by (rtac bexI 1); 
 by (assume_tac 2);
 by (Blast_tac 1);
 qed "reachable_transient";
 
-(*Uses the premise "invariant (Init,Acts)".  Raw theorem-proving on this
+(*Uses the premise "invariant prg".  Raw theorem-proving on this
   inclusion is slow: the term contains a copy of the program.*)
-Goal "[| invariant (Init,Acts) INV;      \
-\        constrains Acts (INV Int (A - A')) (A Un A'); \
-\        transient  Acts (INV Int (A-A')) |]   \
-\     ==> LeadsTo(Init,Acts) A A'";
+Goal "[| invariant prg INV;      \
+\        constrains (Acts prg) (INV Int (A-A')) (A Un A'); \
+\        transient  (Acts prg) (INV Int (A-A')) |]   \
+\ ==> ensures (Acts prg) (reachable prg Int A) (reachable prg Int A')";
 bd invariant_includes_reachable 1;
-by (rtac LeadsTo_Basis 1);
+by (rtac ensuresI 1);
+by (ALLGOALS 
+    (full_simp_tac (simpset() addsimps [Int_Un_distrib RS sym, 
+					Diff_Int_distrib RS sym])));
 by (blast_tac (claset() addSIs [reachable_transient]) 2);
-by (rewtac constrains_def);
-by (Blast_tac 1);
-qed "invariant_LeadsTo_Basis";
+br (stable_reachable RS stable_constrains_Int) 1;
+by (blast_tac (claset() addIs [constrains_weaken]) 1);
+qed "invariant_ensuresI";
+
+bind_thm ("invariant_LeadsTo_Basis", invariant_ensuresI RS LeadsTo_Basis);
 
 
-Goal "[| invariant (Init,Acts) INV;      \
-\        LeadsTo(Init,Acts) A A'; id: Acts;   \
+Goal "[| invariant prg INV;      \
+\        LeadsTo prg A A'; id: (Acts prg);   \
 \        INV Int B  <= A;  INV Int A' <= B' |] \
-\     ==> LeadsTo(Init,Acts) B B'";
+\     ==> LeadsTo prg B B'";
 by (blast_tac (claset() addDs [invariant_includes_reachable]
 			addIs [LeadsTo_weaken]) 1);
 qed "invariant_LeadsTo_weaken";
@@ -425,8 +427,8 @@
    SELECT_GOAL
       (EVERY [TRY (rtac stableI 1),
 	      rtac constrainsI 1,
-	      rewtac main_def,
-	      REPEAT_FIRST (eresolve_tac [insertE, emptyE]),
+	      full_simp_tac (simpset() addsimps [main_def]) 1,
+	      REPEAT_FIRST (eresolve_tac [disjE]),
 	      rewrite_goals_tac cmd_defs,
 	      ALLGOALS (SELECT_GOAL Auto_tac)]);
 
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/SubstAx.thy
--- a/src/HOL/UNITY/SubstAx.thy	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/SubstAx.thy	Wed Aug 05 10:57:25 1998 +0200
@@ -10,10 +10,9 @@
 
 constdefs
 
-   LeadsTo :: "['a set * ('a * 'a)set set, 'a set, 'a set] => bool"
-    "LeadsTo == %(Init,Acts) A B.
-		 leadsTo Acts (reachable (Init,Acts) Int A)
-			      (reachable (Init,Acts) Int B)"
-
-
+   LeadsTo :: "['a program, 'a set, 'a set] => bool"
+    "LeadsTo prg A B ==
+		 leadsTo (Acts prg)
+                         (reachable prg  Int  A)
+  		         (reachable prg  Int  B)"
 end
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/Token.ML
--- a/src/HOL/UNITY/Token.ML	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Token.ML	Wed Aug 05 10:57:25 1998 +0200
@@ -23,7 +23,7 @@
 qed "not_E_eq";
 
 (*This proof is in the "massaging" style and is much faster! *)
-Goalw [stable_def] "stable Acts (Compl(E i) Un (HasTok i))";
+Goalw [stable_def] "stable acts (Compl(E i) Un (HasTok i))";
 by (rtac constrains_weaken 1);
 by (rtac ([[TR2, TR4] MRS constrains_Un, TR5] MRS constrains_Un) 1);
 by (auto_tac (claset(), simpset() addsimps [not_E_eq]));
@@ -77,7 +77,7 @@
 (*From "A Logic for Concurrent Programming", but not used in Chapter 4.
   Note the use of case_tac.  Reasoning about leadsTo takes practice!*)
 Goal "[| i<N; j<N |] ==>   \
-\     leadsTo Acts (HasTok i) ({s. (token s, i) : nodeOrder j} Un HasTok j)";
+\     leadsTo acts (HasTok i) ({s. (token s, i) : nodeOrder j} Un HasTok j)";
 by (case_tac "i=j" 1);
 by (blast_tac (claset() addIs [subset_imp_leadsTo]) 1);
 by (rtac (TR7 RS leadsTo_weaken_R) 1);
@@ -88,7 +88,7 @@
 
 (*Chapter 4 variant, the one actually used below.*)
 Goal "[| i<N; j<N; i~=j |]    \
-\     ==> leadsTo Acts (HasTok i) {s. (token s, i) : nodeOrder j}";
+\     ==> leadsTo acts (HasTok i) {s. (token s, i) : nodeOrder j}";
 by (rtac (TR7 RS leadsTo_weaken_R) 1);
 by (Clarify_tac 1);
 by (asm_full_simp_tac (simpset() addsimps [HasTok_def, nodeOrder_eq]) 1);
@@ -101,7 +101,7 @@
 
 
 (*Misra's TR9: the token reaches an arbitrary node*)
-Goal "j<N ==> leadsTo Acts {s. token s < N} (HasTok j)";
+Goal "j<N ==> leadsTo acts {s. token s < N} (HasTok j)";
 by (rtac leadsTo_weaken_R 1);
 by (res_inst_tac [("I", "Compl{j}"), ("f", "token"), ("B", "{}")]
      (wf_nodeOrder RS bounded_induct) 1);
@@ -115,7 +115,7 @@
 qed "leadsTo_j";
 
 (*Misra's TR8: a hungry process eventually eats*)
-Goal "j<N ==> leadsTo Acts ({s. token s < N} Int H j) (E j)";
+Goal "j<N ==> leadsTo acts ({s. token s < N} Int H j) (E j)";
 by (rtac (leadsTo_cancel1 RS leadsTo_Un_duplicate) 1);
 by (rtac TR6 2);
 by (rtac leadsTo_weaken_R 1);
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/Token.thy
--- a/src/HOL/UNITY/Token.thy	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Token.thy	Wed Aug 05 10:57:25 1998 +0200
@@ -44,18 +44,18 @@
 rules
   N_positive "0<N"
 
-  skip "id: Acts"
+  skip "id: acts"
 
-  TR2  "constrains Acts (T i) (T i Un H i)"
+  TR2  "constrains acts (T i) (T i Un H i)"
 
-  TR3  "constrains Acts (H i) (H i Un E i)"
+  TR3  "constrains acts (H i) (H i Un E i)"
 
-  TR4  "constrains Acts (H i - HasTok i) (H i)"
+  TR4  "constrains acts (H i - HasTok i) (H i)"
 
-  TR5  "constrains Acts (HasTok i) (HasTok i Un Compl(E i))"
+  TR5  "constrains acts (HasTok i) (HasTok i Un Compl(E i))"
 
-  TR6  "leadsTo Acts (H i Int HasTok i) (E i)"
+  TR6  "leadsTo acts (H i Int HasTok i) (E i)"
 
-  TR7  "leadsTo Acts (HasTok i) (HasTok (next i))"
+  TR7  "leadsTo acts (HasTok i) (HasTok (next i))"
 
 end
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/Traces.ML
--- a/src/HOL/UNITY/Traces.ML	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Traces.ML	Wed Aug 05 10:57:25 1998 +0200
@@ -9,74 +9,25 @@
 
 *)
 
-(****
-Now simulate the inductive definition (illegal due to paired arguments)
-
-inductive "reachable(Init,Acts)"
-  intrs 
-    Init  "s: Init ==> s : reachable(Init,Acts)"
-
-    Acts  "[| act: Acts;  s : reachable(Init,Acts);  (s,s'): act |]
-	   ==> s' : reachable(Init,Acts)"
-
-This amounts to an equivalence proof for the definition actually used, 
-****)
-
-
-(** reachable: Deriving the Introduction rules **)
-
-Goal "s: Init ==> s : reachable(Init,Acts)";
-by (simp_tac (simpset() addsimps [reachable_def]) 1);
-by (blast_tac (claset() addIs traces.intrs) 1);
-qed "reachable_Init";
-
+Goal "reachable prg = {s. EX evs. (s,evs): traces (Init prg) (Acts prg)}";
+by Safe_tac;
+by (etac traces.induct 2);
+be reachable.induct 1;
+by (ALLGOALS (blast_tac (claset() addIs (reachable.intrs @ traces.intrs))));
+qed "reachable_equiv_traces";
 
-Goal "[| act: Acts;  s : reachable(Init,Acts) |] \
-\     ==> (s,s'): act --> s' : reachable(Init,Acts)";
-by (asm_full_simp_tac (simpset() addsimps [reachable_def]) 1);
-by (etac exE 1);
-by (etac traces.induct 1);
-by (ALLGOALS Asm_simp_tac);
-by (ALLGOALS (blast_tac (claset() addIs traces.intrs)));
-qed_spec_mp "reachable_Acts";
-
-
-val major::prems = 
-Goalw [reachable_def] 
-  "[| za : reachable(Init,Acts);  \
-\     !!s. s : Init ==> P s;      \
-\     !!act s s'.  \
-\        [| act : Acts; s : reachable(Init,Acts); P s; (s, s') : act |]  \
-\        ==> P s' |] \
-\  ==> P za";
-by (cut_facts_tac [major] 1);
-by Auto_tac;
-by (etac traces.induct 1);
-by (ALLGOALS (blast_tac (claset() addIs prems)));
-qed "reachable_induct";
-
-structure reachable = 
-  struct 
-  val Init = reachable_Init
-  val Acts = reachable_Acts
-  val intrs = [reachable_Init, reachable_Acts]
-  val induct = reachable_induct
-  end;
-
-
-
-Goal "stable Acts (reachable(Init,Acts))";
+Goal "stable (Acts prg) (reachable prg)";
 by (blast_tac (claset() addIs ([stableI, constrainsI] @ reachable.intrs)) 1);
 qed "stable_reachable";
 
 (*The set of all reachable states is an invariant...*)
-Goal "invariant (Init,Acts) (reachable(Init,Acts))";
+Goal "invariant prg (reachable prg)";
 by (simp_tac (simpset() addsimps [invariant_def]) 1);
 by (blast_tac (claset() addIs (stable_reachable::reachable.intrs)) 1);
 qed "invariant_reachable";
 
 (*...in fact the strongest invariant!*)
-Goal "invariant (Init,Acts) A ==> reachable(Init,Acts) <= A";
+Goal "invariant prg A ==> reachable prg <= A";
 by (full_simp_tac 
     (simpset() addsimps [stable_def, constrains_def, invariant_def]) 1);
 by (rtac subsetI 1);
@@ -86,15 +37,15 @@
 
 (*If "A" includes the initial states and is stable then "A" is invariant.
   Result is trivial from the definition, but it is handy.*)
-Goal "[| Init<=A;  stable Acts A |] ==> invariant (Init,Acts) A";
+Goal "[| (Init prg)<=A;  stable (Acts prg) A |] ==> invariant prg A";
 by (asm_simp_tac (simpset() addsimps [invariant_def]) 1);
 qed "invariantI";
 
 
 (** Conjoining invariants **)
 
-Goal "[| invariant (Init,Acts) A;  invariant (Init,Acts) B |] \
-\     ==> invariant (Init,Acts) (A Int B)";
+Goal "[| invariant prg A;  invariant prg B |] \
+\     ==> invariant prg (A Int B)";
 by (asm_full_simp_tac (simpset() addsimps [invariant_def, stable_Int]) 1);
 by Auto_tac;
 qed "invariant_Int";
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/Traces.thy
--- a/src/HOL/UNITY/Traces.thy	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Traces.thy	Wed Aug 05 10:57:25 1998 +0200
@@ -24,11 +24,22 @@
 	   ==> (s', s#evs) : traces Init Acts"
 
 
+record 'a program =
+  Init :: 'a set
+  Acts :: "('a * 'a)set set"
+
+
+consts reachable :: "'a program => 'a set"
+
+inductive "reachable prg"
+  intrs 
+    Init  "s: Init prg ==> s : reachable prg"
+
+    Acts  "[| act: Acts prg;  s : reachable prg;  (s,s'): act |]
+	   ==> s' : reachable prg"
+
 constdefs
-  reachable :: "'a set * ('a * 'a)set set => 'a set"
-  "reachable == %(Init,Acts). {s. EX evs. (s,evs): traces Init Acts}"
-
-  invariant :: "['a set * ('a * 'a)set set, 'a set] => bool"
-  "invariant == %(Init,Acts) A. Init <= A & stable Acts A"
+  invariant :: "['a program, 'a set] => bool"
+  "invariant prg A == (Init prg) <= A & stable (Acts prg) A"
 
 end
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/UNITY.ML
--- a/src/HOL/UNITY/UNITY.ML	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/UNITY.ML	Wed Aug 05 10:57:25 1998 +0200
@@ -15,97 +15,97 @@
 (*** constrains ***)
 
 val prems = goalw thy [constrains_def]
-    "(!!act s s'. [| act: Acts;  (s,s') : act;  s: A |] ==> s': A') \
-\    ==> constrains Acts A A'";
+    "(!!act s s'. [| act: acts;  (s,s') : act;  s: A |] ==> s': A') \
+\    ==> constrains acts A A'";
 by (blast_tac (claset() addIs prems) 1);
 qed "constrainsI";
 
 Goalw [constrains_def]
-    "[| constrains Acts A A'; act: Acts;  (s,s'): act;  s: A |] \
+    "[| constrains acts A A'; act: acts;  (s,s'): act;  s: A |] \
 \            ==> s': A'";
 by (Blast_tac 1);
 qed "constrainsD";
 
-Goalw [constrains_def] "constrains Acts {} B";
+Goalw [constrains_def] "constrains acts {} B";
 by (Blast_tac 1);
 qed "constrains_empty";
 
-Goalw [constrains_def] "constrains Acts A UNIV";
+Goalw [constrains_def] "constrains acts A UNIV";
 by (Blast_tac 1);
 qed "constrains_UNIV";
 AddIffs [constrains_empty, constrains_UNIV];
 
 Goalw [constrains_def]
-    "[| constrains Acts A A'; A'<=B' |] ==> constrains Acts A B'";
+    "[| constrains acts A A'; A'<=B' |] ==> constrains acts A B'";
 by (Blast_tac 1);
 qed "constrains_weaken_R";
 
 Goalw [constrains_def]
-    "[| constrains Acts A A'; B<=A |] ==> constrains Acts B A'";
+    "[| constrains acts A A'; B<=A |] ==> constrains acts B A'";
 by (Blast_tac 1);
 qed "constrains_weaken_L";
 
 Goalw [constrains_def]
-   "[| constrains Acts A A'; B<=A; A'<=B' |] ==> constrains Acts B B'";
+   "[| constrains acts A A'; B<=A; A'<=B' |] ==> constrains acts B B'";
 by (Blast_tac 1);
 qed "constrains_weaken";
 
 (*Set difference: UNUSED*)
 Goalw [constrains_def]
-  "[| constrains Acts (A-B) C; constrains Acts B C |] \
-\       ==> constrains Acts A C";
+  "[| constrains acts (A-B) C; constrains acts B C |] \
+\       ==> constrains acts A C";
 by (Blast_tac 1);
 qed "constrains_Diff";
 
 (** Union **)
 
 Goalw [constrains_def]
-    "[| constrains Acts A A'; constrains Acts B B' |]   \
-\           ==> constrains Acts (A Un B) (A' Un B')";
+    "[| constrains acts A A'; constrains acts B B' |]   \
+\           ==> constrains acts (A Un B) (A' Un B')";
 by (Blast_tac 1);
 qed "constrains_Un";
 
 Goalw [constrains_def]
-    "ALL i:I. constrains Acts (A i) (A' i) \
-\    ==> constrains Acts (UN i:I. A i) (UN i:I. A' i)";
+    "ALL i:I. constrains acts (A i) (A' i) \
+\    ==> constrains acts (UN i:I. A i) (UN i:I. A' i)";
 by (Blast_tac 1);
 qed "ball_constrains_UN";
 
 Goalw [constrains_def]
-    "[| ALL i. constrains Acts (A i) (A' i) |] \
-\           ==> constrains Acts (UN i. A i) (UN i. A' i)";
+    "[| ALL i. constrains acts (A i) (A' i) |] \
+\           ==> constrains acts (UN i. A i) (UN i. A' i)";
 by (Blast_tac 1);
 qed "all_constrains_UN";
 
 (** Intersection **)
 
 Goalw [constrains_def]
-    "[| constrains Acts A A'; constrains Acts B B' |]   \
-\           ==> constrains Acts (A Int B) (A' Int B')";
+    "[| constrains acts A A'; constrains acts B B' |]   \
+\           ==> constrains acts (A Int B) (A' Int B')";
 by (Blast_tac 1);
 qed "constrains_Int";
 
 Goalw [constrains_def]
-    "ALL i:I. constrains Acts (A i) (A' i) \
-\    ==> constrains Acts (INT i:I. A i) (INT i:I. A' i)";
+    "ALL i:I. constrains acts (A i) (A' i) \
+\    ==> constrains acts (INT i:I. A i) (INT i:I. A' i)";
 by (Blast_tac 1);
 qed "ball_constrains_INT";
 
 Goalw [constrains_def]
-    "[| ALL i. constrains Acts (A i) (A' i) |] \
-\           ==> constrains Acts (INT i. A i) (INT i. A' i)";
+    "[| ALL i. constrains acts (A i) (A' i) |] \
+\           ==> constrains acts (INT i. A i) (INT i. A' i)";
 by (Blast_tac 1);
 qed "all_constrains_INT";
 
 Goalw [stable_def, constrains_def]
-    "[| stable Acts C; constrains Acts A (C Un A') |]   \
-\           ==> constrains Acts (C Un A) (C Un A')";
+    "[| stable acts C; constrains acts A (C Un A') |]   \
+\           ==> constrains acts (C Un A) (C Un A')";
 by (Blast_tac 1);
 qed "stable_constrains_Un";
 
 Goalw [stable_def, constrains_def]
-    "[| stable Acts C; constrains Acts (C Int A) A' |]   \
-\           ==> constrains Acts (C Int A) (C Int A')";
+    "[| stable acts C; constrains acts (C Int A) A' |]   \
+\           ==> constrains acts (C Int A) (C Int A')";
 by (Blast_tac 1);
 qed "stable_constrains_Int";
 
@@ -113,36 +113,36 @@
 (*** stable ***)
 
 Goalw [stable_def]
-    "constrains Acts A A ==> stable Acts A";
+    "constrains acts A A ==> stable acts A";
 by (assume_tac 1);
 qed "stableI";
 
 Goalw [stable_def]
-    "stable Acts A ==> constrains Acts A A";
+    "stable acts A ==> constrains acts A A";
 by (assume_tac 1);
 qed "stableD";
 
 Goalw [stable_def]
-    "[| stable Acts A; stable Acts A' |]   \
-\           ==> stable Acts (A Un A')";
+    "[| stable acts A; stable acts A' |]   \
+\           ==> stable acts (A Un A')";
 by (blast_tac (claset() addIs [constrains_Un]) 1);
 qed "stable_Un";
 
 Goalw [stable_def]
-    "[| stable Acts A; stable Acts A' |]   \
-\           ==> stable Acts (A Int A')";
+    "[| stable acts A; stable acts A' |]   \
+\           ==> stable acts (A Int A')";
 by (blast_tac (claset() addIs [constrains_Int]) 1);
 qed "stable_Int";
 
 Goalw [constrains_def]
-    "[| constrains Acts A A'; id: Acts |] ==> A<=A'";
+    "[| constrains acts A A'; id: acts |] ==> A<=A'";
 by (Blast_tac 1);
 qed "constrains_imp_subset";
 
 
 Goalw [constrains_def]
-    "[| id: Acts; constrains Acts A B; constrains Acts B C |]   \
-\           ==> constrains Acts A C";
+    "[| id: acts; constrains acts A B; constrains acts B C |]   \
+\           ==> constrains acts A C";
 by (Blast_tac 1);
 qed "constrains_trans";
 
@@ -151,23 +151,23 @@
   Should the premise be !!m instead of ALL m ?  Would make it harder to use
   in forward proof.*)
 Goalw [constrains_def]
-    "[| ALL m. constrains Acts {s. s x = m} (B m) |] \
-\           ==> constrains Acts {s. P(s x)} (UN m. {s. P(m)} Int B m)";
+    "[| ALL m. constrains acts {s. s x = m} (B m) |] \
+\           ==> constrains acts {s. P(s x)} (UN m. {s. P(m)} Int B m)";
 by (Blast_tac 1);
 qed "elimination";
 
 (*As above, but for the trivial case of a one-variable state, in which the
   state is identified with its one variable.*)
 Goalw [constrains_def]
-    "[| ALL m. constrains Acts {m} (B m) |] \
-\           ==> constrains Acts {s. P s} (UN m. {s. P(m)} Int B m)";
+    "[| ALL m. constrains acts {m} (B m) |] \
+\           ==> constrains acts {s. P s} (UN m. {s. P(m)} Int B m)";
 by (Blast_tac 1);
 qed "elimination_sing";
 
 
 Goalw [constrains_def]
-   "[| constrains Acts A (A' Un B); constrains Acts B B'; id: Acts |] \
-\           ==> constrains Acts A (A' Un B')";
+   "[| constrains acts A (A' Un B); constrains acts B B'; id: acts |] \
+\           ==> constrains acts A (A' Un B')";
 by (Blast_tac 1);
 qed "constrains_cancel";
 
@@ -176,11 +176,11 @@
 (*** Theoretical Results from Section 6 ***)
 
 Goalw [constrains_def, strongest_rhs_def]
-    "constrains Acts A (strongest_rhs Acts A )";
+    "constrains acts A (strongest_rhs acts A )";
 by (Blast_tac 1);
 qed "constrains_strongest_rhs";
 
 Goalw [constrains_def, strongest_rhs_def]
-    "constrains Acts A B ==> strongest_rhs Acts A <= B";
+    "constrains acts A B ==> strongest_rhs acts A <= B";
 by (Blast_tac 1);
 qed "strongest_rhs_is_strongest";
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/UNITY.thy
--- a/src/HOL/UNITY/UNITY.thy	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/UNITY.thy	Wed Aug 05 10:57:25 1998 +0200
@@ -13,15 +13,15 @@
 constdefs
 
   constrains :: "[('a * 'a)set set, 'a set, 'a set] => bool"
-    "constrains Acts A B == ALL act:Acts. act^^A <= B"
+    "constrains acts A B == ALL act:acts. act^^A <= B"
 
   stable     :: "('a * 'a)set set => 'a set => bool"
-    "stable Acts A == constrains Acts A A"
+    "stable acts A == constrains acts A A"
 
   strongest_rhs :: "[('a * 'a)set set, 'a set] => 'a set"
-    "strongest_rhs Acts A == Inter {B. constrains Acts A B}"
+    "strongest_rhs acts A == Inter {B. constrains acts A B}"
 
   unless :: "[('a * 'a)set set, 'a set, 'a set] => bool"
-    "unless Acts A B == constrains Acts (A-B) (A Un B)"
+    "unless acts A B == constrains acts (A-B) (A Un B)"
 
 end
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/WFair.ML
--- a/src/HOL/UNITY/WFair.ML	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/WFair.ML	Wed Aug 05 10:57:25 1998 +0200
@@ -12,20 +12,20 @@
 (*** transient ***)
 
 Goalw [stable_def, constrains_def, transient_def]
-    "[| stable Acts A; transient Acts A |] ==> A = {}";
+    "[| stable acts A; transient acts A |] ==> A = {}";
 by (Blast_tac 1);
 qed "stable_transient_empty";
 
 Goalw [transient_def]
-    "[| transient Acts A; B<=A |] ==> transient Acts B";
+    "[| transient acts A; B<=A |] ==> transient acts B";
 by (Clarify_tac 1);
 by (rtac bexI 1 THEN assume_tac 2);
 by (Blast_tac 1);
 qed "transient_strengthen";
 
 Goalw [transient_def]
-    "[| act:Acts;  A <= Domain act;  act^^A <= Compl A |] \
-\         ==> transient Acts A";
+    "[| act:acts;  A <= Domain act;  act^^A <= Compl A |] \
+\         ==> transient acts A";
 by (Blast_tac 1);
 qed "transient_mem";
 
@@ -33,34 +33,34 @@
 (*** ensures ***)
 
 Goalw [ensures_def]
-    "[| constrains Acts (A-B) (A Un B); transient Acts (A-B) |] \
-\    ==> ensures Acts A B";
+    "[| constrains acts (A-B) (A Un B); transient acts (A-B) |] \
+\    ==> ensures acts A B";
 by (Blast_tac 1);
 qed "ensuresI";
 
 Goalw [ensures_def]
-    "ensures Acts A B  \
-\    ==> constrains Acts (A-B) (A Un B) & transient Acts (A-B)";
+    "ensures acts A B  \
+\    ==> constrains acts (A-B) (A Un B) & transient acts (A-B)";
 by (Blast_tac 1);
 qed "ensuresD";
 
 (*The L-version (precondition strengthening) doesn't hold for ENSURES*)
 Goalw [ensures_def]
-    "[| ensures Acts A A'; A'<=B' |] ==> ensures Acts A B'";
+    "[| ensures acts A A'; A'<=B' |] ==> ensures acts A B'";
 by (blast_tac (claset() addIs [constrains_weaken, transient_strengthen]) 1);
 qed "ensures_weaken_R";
 
 Goalw [ensures_def, constrains_def, transient_def]
-    "Acts ~= {} ==> ensures Acts A UNIV";
+    "acts ~= {} ==> ensures acts A UNIV";
 by (Asm_simp_tac 1);  (*omitting this causes PROOF FAILED, even with Safe_tac*)
 by (Blast_tac 1);
 qed "ensures_UNIV";
 
 Goalw [ensures_def]
-    "[| stable Acts C; \
-\       constrains Acts (C Int (A - A')) (A Un A'); \
-\       transient  Acts (C Int (A-A')) |]   \
-\   ==> ensures Acts (C Int A) (C Int A')";
+    "[| stable acts C; \
+\       constrains acts (C Int (A - A')) (A Un A'); \
+\       transient  acts (C Int (A-A')) |]   \
+\   ==> ensures acts (C Int A) (C Int A')";
 by (asm_simp_tac (simpset() addsimps [Int_Un_distrib RS sym,
 				      Diff_Int_distrib RS sym,
 				      stable_constrains_Int]) 1);
@@ -73,34 +73,34 @@
 bind_thm ("leadsTo_Basis", leadsto.Basis);
 bind_thm ("leadsTo_Trans", leadsto.Trans);
 
-Goal "act: Acts ==> leadsTo Acts A UNIV";
+Goal "act: acts ==> leadsTo acts A UNIV";
 by (blast_tac (claset() addIs [ensures_UNIV RS leadsTo_Basis]) 1);
 qed "leadsTo_UNIV";
 Addsimps [leadsTo_UNIV];
 
 (*Useful with cancellation, disjunction*)
-Goal "leadsTo Acts A (A' Un A') ==> leadsTo Acts A A'";
+Goal "leadsTo acts A (A' Un A') ==> leadsTo acts A A'";
 by (asm_full_simp_tac (simpset() addsimps Un_ac) 1);
 qed "leadsTo_Un_duplicate";
 
-Goal "leadsTo Acts A (A' Un C Un C) ==> leadsTo Acts A (A' Un C)";
+Goal "leadsTo acts A (A' Un C Un C) ==> leadsTo acts A (A' Un C)";
 by (asm_full_simp_tac (simpset() addsimps Un_ac) 1);
 qed "leadsTo_Un_duplicate2";
 
 (*The Union introduction rule as we should have liked to state it*)
 val prems = goal thy
-    "(!!A. A : S ==> leadsTo Acts A B) ==> leadsTo Acts (Union S) B";
+    "(!!A. A : S ==> leadsTo acts A B) ==> leadsTo acts (Union S) B";
 by (blast_tac (claset() addIs (leadsto.Union::prems)) 1);
 qed "leadsTo_Union";
 
 val prems = goal thy
-    "(!!i. i : I ==> leadsTo Acts (A i) B) ==> leadsTo Acts (UN i:I. A i) B";
+    "(!!i. i : I ==> leadsTo acts (A i) B) ==> leadsTo acts (UN i:I. A i) B";
 by (simp_tac (simpset() addsimps [Union_image_eq RS sym]) 1);
 by (blast_tac (claset() addIs (leadsto.Union::prems)) 1);
 qed "leadsTo_UN";
 
 (*Binary union introduction rule*)
-Goal "[| leadsTo Acts A C; leadsTo Acts B C |] ==> leadsTo Acts (A Un B) C";
+Goal "[| leadsTo acts A C; leadsTo acts B C |] ==> leadsTo acts (A Un B) C";
 by (stac Un_eq_Union 1);
 by (blast_tac (claset() addIs [leadsTo_Union]) 1);
 qed "leadsTo_Un";
@@ -108,18 +108,18 @@
 
 (*The INDUCTION rule as we should have liked to state it*)
 val major::prems = goal thy
-  "[| leadsTo Acts za zb;  \
-\     !!A B. ensures Acts A B ==> P A B; \
-\     !!A B C. [| leadsTo Acts A B; P A B; leadsTo Acts B C; P B C |] \
+  "[| leadsTo acts za zb;  \
+\     !!A B. ensures acts A B ==> P A B; \
+\     !!A B C. [| leadsTo acts A B; P A B; leadsTo acts B C; P B C |] \
 \              ==> P A C; \
-\     !!B S. ALL A:S. leadsTo Acts A B & P A B ==> P (Union S) B \
+\     !!B S. ALL A:S. leadsTo acts A B & P A B ==> P (Union S) B \
 \  |] ==> P za zb";
 by (rtac (major RS leadsto.induct) 1);
 by (REPEAT (blast_tac (claset() addIs prems) 1));
 qed "leadsTo_induct";
 
 
-Goal "[| A<=B;  id: Acts |] ==> leadsTo Acts A B";
+Goal "[| A<=B;  id: acts |] ==> leadsTo acts A B";
 by (rtac leadsTo_Basis 1);
 by (rewrite_goals_tac [ensures_def, constrains_def, transient_def]);
 by (Blast_tac 1);
@@ -130,8 +130,8 @@
 
 
 (*There's a direct proof by leadsTo_Trans and subset_imp_leadsTo, but it
-  needs the extra premise id:Acts*)
-Goal "leadsTo Acts A A' ==> A'<=B' --> leadsTo Acts A B'";
+  needs the extra premise id:acts*)
+Goal "leadsTo acts A A' ==> A'<=B' --> leadsTo acts A B'";
 by (etac leadsTo_induct 1);
 by (Clarify_tac 3);
 by (blast_tac (claset() addIs [leadsTo_Union]) 3);
@@ -140,31 +140,31 @@
 qed_spec_mp "leadsTo_weaken_R";
 
 
-Goal "[| leadsTo Acts A A'; B<=A; id: Acts |] ==>  \
-\         leadsTo Acts B A'";
+Goal "[| leadsTo acts A A'; B<=A; id: acts |] ==>  \
+\         leadsTo acts B A'";
 by (blast_tac (claset() addIs [leadsTo_Basis, leadsTo_Trans, 
 			       subset_imp_leadsTo]) 1);
 qed_spec_mp "leadsTo_weaken_L";
 
 (*Distributes over binary unions*)
-Goal "id: Acts ==> \
-\       leadsTo Acts (A Un B) C  =  (leadsTo Acts A C & leadsTo Acts B C)";
+Goal "id: acts ==> \
+\       leadsTo acts (A Un B) C  =  (leadsTo acts A C & leadsTo acts B C)";
 by (blast_tac (claset() addIs [leadsTo_Un, leadsTo_weaken_L]) 1);
 qed "leadsTo_Un_distrib";
 
-Goal "id: Acts ==> \
-\       leadsTo Acts (UN i:I. A i) B  =  (ALL i : I. leadsTo Acts (A i) B)";
+Goal "id: acts ==> \
+\       leadsTo acts (UN i:I. A i) B  =  (ALL i : I. leadsTo acts (A i) B)";
 by (blast_tac (claset() addIs [leadsTo_UN, leadsTo_weaken_L]) 1);
 qed "leadsTo_UN_distrib";
 
-Goal "id: Acts ==> \
-\       leadsTo Acts (Union S) B  =  (ALL A : S. leadsTo Acts A B)";
+Goal "id: acts ==> \
+\       leadsTo acts (Union S) B  =  (ALL A : S. leadsTo acts A B)";
 by (blast_tac (claset() addIs [leadsTo_Union, leadsTo_weaken_L]) 1);
 qed "leadsTo_Union_distrib";
 
 
-Goal "[| leadsTo Acts A A'; id: Acts; B<=A; A'<=B' |] \
-\   ==> leadsTo Acts B B'";
+Goal "[| leadsTo acts A A'; id: acts; B<=A; A'<=B' |] \
+\   ==> leadsTo acts B B'";
 (*PROOF FAILED: why?*)
 by (blast_tac (claset() addIs [leadsTo_Trans, leadsTo_weaken_R,
 			       leadsTo_weaken_L]) 1);
@@ -172,8 +172,8 @@
 
 
 (*Set difference: maybe combine with leadsTo_weaken_L??*)
-Goal "[| leadsTo Acts (A-B) C; leadsTo Acts B C; id: Acts |] \
-\       ==> leadsTo Acts A C";
+Goal "[| leadsTo acts (A-B) C; leadsTo acts B C; id: acts |] \
+\       ==> leadsTo acts A C";
 by (blast_tac (claset() addIs [leadsTo_Un, leadsTo_weaken]) 1);
 qed "leadsTo_Diff";
 
@@ -182,8 +182,8 @@
     see ball_constrains_UN in UNITY.ML***)
 
 val prems = goal thy
-   "(!! i. i:I ==> leadsTo Acts (A i) (A' i)) \
-\   ==> leadsTo Acts (UN i:I. A i) (UN i:I. A' i)";
+   "(!! i. i:I ==> leadsTo acts (A i) (A' i)) \
+\   ==> leadsTo acts (UN i:I. A i) (UN i:I. A' i)";
 by (simp_tac (simpset() addsimps [Union_image_eq RS sym]) 1);
 by (blast_tac (claset() addIs [leadsTo_Union, leadsTo_weaken_R] 
                         addIs prems) 1);
@@ -192,22 +192,22 @@
 
 (*Version with no index set*)
 val prems = goal thy
-   "(!! i. leadsTo Acts (A i) (A' i)) \
-\   ==> leadsTo Acts (UN i. A i) (UN i. A' i)";
+   "(!! i. leadsTo acts (A i) (A' i)) \
+\   ==> leadsTo acts (UN i. A i) (UN i. A' i)";
 by (blast_tac (claset() addIs [leadsTo_UN_UN] 
                         addIs prems) 1);
 qed "leadsTo_UN_UN_noindex";
 
 (*Version with no index set*)
-Goal "ALL i. leadsTo Acts (A i) (A' i) \
-\   ==> leadsTo Acts (UN i. A i) (UN i. A' i)";
+Goal "ALL i. leadsTo acts (A i) (A' i) \
+\   ==> leadsTo acts (UN i. A i) (UN i. A' i)";
 by (blast_tac (claset() addIs [leadsTo_UN_UN]) 1);
 qed "all_leadsTo_UN_UN";
 
 
 (*Binary union version*)
-Goal "[| leadsTo Acts A A'; leadsTo Acts B B' |] \
-\         ==> leadsTo Acts (A Un B) (A' Un B')";
+Goal "[| leadsTo acts A A'; leadsTo acts B B' |] \
+\         ==> leadsTo acts (A Un B) (A' Un B')";
 by (blast_tac (claset() addIs [leadsTo_Un, 
 			       leadsTo_weaken_R]) 1);
 qed "leadsTo_Un_Un";
@@ -215,27 +215,27 @@
 
 (** The cancellation law **)
 
-Goal "[| leadsTo Acts A (A' Un B); leadsTo Acts B B'; id: Acts |] \
-\   ==> leadsTo Acts A (A' Un B')";
+Goal "[| leadsTo acts A (A' Un B); leadsTo acts B B'; id: acts |] \
+\   ==> leadsTo acts A (A' Un B')";
 by (blast_tac (claset() addIs [leadsTo_Un_Un, 
 			       subset_imp_leadsTo, leadsTo_Trans]) 1);
 qed "leadsTo_cancel2";
 
-Goal "[| leadsTo Acts A (A' Un B); leadsTo Acts (B-A') B'; id: Acts |] \
-\   ==> leadsTo Acts A (A' Un B')";
+Goal "[| leadsTo acts A (A' Un B); leadsTo acts (B-A') B'; id: acts |] \
+\   ==> leadsTo acts A (A' Un B')";
 by (rtac leadsTo_cancel2 1);
 by (assume_tac 2);
 by (ALLGOALS Asm_simp_tac);
 qed "leadsTo_cancel_Diff2";
 
-Goal "[| leadsTo Acts A (B Un A'); leadsTo Acts B B'; id: Acts |] \
-\   ==> leadsTo Acts A (B' Un A')";
+Goal "[| leadsTo acts A (B Un A'); leadsTo acts B B'; id: acts |] \
+\   ==> leadsTo acts A (B' Un A')";
 by (asm_full_simp_tac (simpset() addsimps [Un_commute]) 1);
 by (blast_tac (claset() addSIs [leadsTo_cancel2]) 1);
 qed "leadsTo_cancel1";
 
-Goal "[| leadsTo Acts A (B Un A'); leadsTo Acts (B-A') B'; id: Acts |] \
-\   ==> leadsTo Acts A (B' Un A')";
+Goal "[| leadsTo acts A (B Un A'); leadsTo acts (B-A') B'; id: acts |] \
+\   ==> leadsTo acts A (B' Un A')";
 by (rtac leadsTo_cancel1 1);
 by (assume_tac 2);
 by (ALLGOALS Asm_simp_tac);
@@ -245,24 +245,24 @@
 
 (** The impossibility law **)
 
-Goal "leadsTo Acts A B ==> B={} --> A={}";
+Goal "leadsTo acts A B ==> B={} --> A={}";
 by (etac leadsTo_induct 1);
 by (ALLGOALS Asm_simp_tac);
 by (rewrite_goals_tac [ensures_def, constrains_def, transient_def]);
 by (Blast_tac 1);
 val lemma = result() RS mp;
 
-Goal "leadsTo Acts A {} ==> A={}";
+Goal "leadsTo acts A {} ==> A={}";
 by (blast_tac (claset() addSIs [lemma]) 1);
 qed "leadsTo_empty";
 
 
 (** PSP: Progress-Safety-Progress **)
 
-(*Special case of PSP: Misra's "stable conjunction".  Doesn't need id:Acts. *)
+(*Special case of PSP: Misra's "stable conjunction".  Doesn't need id:acts. *)
 Goalw [stable_def]
-   "[| leadsTo Acts A A'; stable Acts B |] \
-\   ==> leadsTo Acts (A Int B) (A' Int B)";
+   "[| leadsTo acts A A'; stable acts B |] \
+\   ==> leadsTo acts (A Int B) (A' Int B)";
 by (etac leadsTo_induct 1);
 by (simp_tac (simpset() addsimps [Int_Union_Union]) 3);
 by (blast_tac (claset() addIs [leadsTo_Union]) 3);
@@ -274,15 +274,15 @@
 by (blast_tac (claset() addIs [transient_strengthen, constrains_Int]) 1);
 qed "PSP_stable";
 
-Goal "[| leadsTo Acts A A'; stable Acts B |] \
-\   ==> leadsTo Acts (B Int A) (B Int A')";
+Goal "[| leadsTo acts A A'; stable acts B |] \
+\   ==> leadsTo acts (B Int A) (B Int A')";
 by (asm_simp_tac (simpset() addsimps (PSP_stable::Int_ac)) 1);
 qed "PSP_stable2";
 
 
 Goalw [ensures_def]
-   "[| ensures Acts A A'; constrains Acts B B' |] \
-\   ==> ensures Acts (A Int B) ((A' Int B) Un (B' - B))";
+   "[| ensures acts A A'; constrains acts B B' |] \
+\   ==> ensures acts (A Int B) ((A' Int B) Un (B' - B))";
 by Safe_tac;
 by (blast_tac (claset() addIs [constrainsI] addDs [constrainsD]) 1);
 by (etac transient_strengthen 1);
@@ -290,8 +290,8 @@
 qed "PSP_ensures";
 
 
-Goal "[| leadsTo Acts A A'; constrains Acts B B'; id: Acts |] \
-\           ==> leadsTo Acts (A Int B) ((A' Int B) Un (B' - B))";
+Goal "[| leadsTo acts A A'; constrains acts B B'; id: acts |] \
+\           ==> leadsTo acts (A Int B) ((A' Int B) Un (B' - B))";
 by (etac leadsTo_induct 1);
 by (simp_tac (simpset() addsimps [Int_Union_Union]) 3);
 by (blast_tac (claset() addIs [leadsTo_Union]) 3);
@@ -304,15 +304,15 @@
 by (blast_tac (claset() addIs [leadsTo_Basis, PSP_ensures]) 1);
 qed "PSP";
 
-Goal "[| leadsTo Acts A A'; constrains Acts B B'; id: Acts |] \
-\   ==> leadsTo Acts (B Int A) ((B Int A') Un (B' - B))";
+Goal "[| leadsTo acts A A'; constrains acts B B'; id: acts |] \
+\   ==> leadsTo acts (B Int A) ((B Int A') Un (B' - B))";
 by (asm_simp_tac (simpset() addsimps (PSP::Int_ac)) 1);
 qed "PSP2";
 
 
 Goalw [unless_def]
-   "[| leadsTo Acts A A'; unless Acts B B'; id: Acts |] \
-\   ==> leadsTo Acts (A Int B) ((A' Int B) Un B')";
+   "[| leadsTo acts A A'; unless acts B B'; id: acts |] \
+\   ==> leadsTo acts (A Int B) ((A' Int B) Un B')";
 by (dtac PSP 1);
 by (assume_tac 1);
 by (asm_full_simp_tac (simpset() addsimps [Un_Diff_Diff, Int_Diff_Un]) 2);
@@ -326,12 +326,12 @@
 (*** Proving the induction rules ***)
 
 Goal "[| wf r;     \
-\        ALL m. leadsTo Acts (A Int f-``{m})                     \
+\        ALL m. leadsTo acts (A Int f-``{m})                     \
 \                            ((A Int f-``(r^-1 ^^ {m})) Un B);   \
-\        id: Acts |] \
-\     ==> leadsTo Acts (A Int f-``{m}) B";
+\        id: acts |] \
+\     ==> leadsTo acts (A Int f-``{m}) B";
 by (eres_inst_tac [("a","m")] wf_induct 1);
-by (subgoal_tac "leadsTo Acts (A Int (f -`` (r^-1 ^^ {x}))) B" 1);
+by (subgoal_tac "leadsTo acts (A Int (f -`` (r^-1 ^^ {x}))) B" 1);
 by (stac vimage_eq_UN 2);
 by (asm_simp_tac (HOL_ss addsimps (UN_simps RL [sym])) 2);
 by (blast_tac (claset() addIs [leadsTo_UN]) 2);
@@ -341,10 +341,10 @@
 
 (** Meta or object quantifier ????? **)
 Goal "[| wf r;     \
-\        ALL m. leadsTo Acts (A Int f-``{m})                     \
+\        ALL m. leadsTo acts (A Int f-``{m})                     \
 \                            ((A Int f-``(r^-1 ^^ {m})) Un B);   \
-\        id: Acts |] \
-\     ==> leadsTo Acts A B";
+\        id: acts |] \
+\     ==> leadsTo acts A B";
 by (res_inst_tac [("t", "A")] subst 1);
 by (rtac leadsTo_UN 2);
 by (etac lemma 2);
@@ -354,10 +354,10 @@
 
 
 Goal "[| wf r;     \
-\        ALL m:I. leadsTo Acts (A Int f-``{m})                   \
+\        ALL m:I. leadsTo acts (A Int f-``{m})                   \
 \                            ((A Int f-``(r^-1 ^^ {m})) Un B);   \
-\        id: Acts |] \
-\     ==> leadsTo Acts A ((A - (f-``I)) Un B)";
+\        id: acts |] \
+\     ==> leadsTo acts A ((A - (f-``I)) Un B)";
 by (etac leadsTo_wf_induct 1);
 by Safe_tac;
 by (case_tac "m:I" 1);
@@ -366,30 +366,30 @@
 qed "bounded_induct";
 
 
-(*Alternative proof is via the lemma leadsTo Acts (A Int f-``(lessThan m)) B*)
-Goal "[| ALL m. leadsTo Acts (A Int f-``{m})                     \
+(*Alternative proof is via the lemma leadsTo acts (A Int f-``(lessThan m)) B*)
+Goal "[| ALL m. leadsTo acts (A Int f-``{m})                     \
 \                            ((A Int f-``(lessThan m)) Un B);   \
-\        id: Acts |] \
-\     ==> leadsTo Acts A B";
+\        id: acts |] \
+\     ==> leadsTo acts A B";
 by (rtac (wf_less_than RS leadsTo_wf_induct) 1);
 by (assume_tac 2);
 by (Asm_simp_tac 1);
 qed "lessThan_induct";
 
-Goal "[| ALL m:(greaterThan l). leadsTo Acts (A Int f-``{m})   \
+Goal "[| ALL m:(greaterThan l). leadsTo acts (A Int f-``{m})   \
 \                                  ((A Int f-``(lessThan m)) Un B);   \
-\        id: Acts |] \
-\     ==> leadsTo Acts A ((A Int (f-``(atMost l))) Un B)";
+\        id: acts |] \
+\     ==> leadsTo acts A ((A Int (f-``(atMost l))) Un B)";
 by (simp_tac (HOL_ss addsimps [Diff_eq RS sym, vimage_Compl, Compl_greaterThan RS sym]) 1);
 by (rtac (wf_less_than RS bounded_induct) 1);
 by (assume_tac 2);
 by (Asm_simp_tac 1);
 qed "lessThan_bounded_induct";
 
-Goal "[| ALL m:(lessThan l). leadsTo Acts (A Int f-``{m})   \
+Goal "[| ALL m:(lessThan l). leadsTo acts (A Int f-``{m})   \
 \                              ((A Int f-``(greaterThan m)) Un B);   \
-\        id: Acts |] \
-\     ==> leadsTo Acts A ((A Int (f-``(atLeast l))) Un B)";
+\        id: acts |] \
+\     ==> leadsTo acts A ((A Int (f-``(atLeast l))) Un B)";
 by (res_inst_tac [("f","f"),("f1", "%k. l - k")]
     (wf_less_than RS wf_inv_image RS leadsTo_wf_induct) 1);
 by (assume_tac 2);
@@ -405,22 +405,22 @@
 (*** wlt ****)
 
 (*Misra's property W3*)
-Goalw [wlt_def] "leadsTo Acts (wlt Acts B) B";
+Goalw [wlt_def] "leadsTo acts (wlt acts B) B";
 by (blast_tac (claset() addSIs [leadsTo_Union]) 1);
 qed "wlt_leadsTo";
 
-Goalw [wlt_def] "leadsTo Acts A B ==> A <= wlt Acts B";
+Goalw [wlt_def] "leadsTo acts A B ==> A <= wlt acts B";
 by (blast_tac (claset() addSIs [leadsTo_Union]) 1);
 qed "leadsTo_subset";
 
 (*Misra's property W2*)
-Goal "id: Acts ==> leadsTo Acts A B = (A <= wlt Acts B)";
+Goal "id: acts ==> leadsTo acts A B = (A <= wlt acts B)";
 by (blast_tac (claset() addSIs [leadsTo_subset, 
 				wlt_leadsTo RS leadsTo_weaken_L]) 1);
 qed "leadsTo_eq_subset_wlt";
 
 (*Misra's property W4*)
-Goal "id: Acts ==> B <= wlt Acts B";
+Goal "id: acts ==> B <= wlt acts B";
 by (asm_simp_tac (simpset() addsimps [leadsTo_eq_subset_wlt RS sym,
 				      subset_imp_leadsTo]) 1);
 qed "wlt_increasing";
@@ -429,17 +429,17 @@
 (*Used in the Trans case below*)
 Goalw [constrains_def]
    "[| B <= A2;  \
-\      constrains Acts (A1 - B) (A1 Un B); \
-\      constrains Acts (A2 - C) (A2 Un C) |] \
-\   ==> constrains Acts (A1 Un A2 - C) (A1 Un A2 Un C)";
+\      constrains acts (A1 - B) (A1 Un B); \
+\      constrains acts (A2 - C) (A2 Un C) |] \
+\   ==> constrains acts (A1 Un A2 - C) (A1 Un A2 Un C)";
 by (Clarify_tac 1);
 by (blast_tac (claset() addSDs [bspec]) 1);
 val lemma1 = result();
 
 
 (*Lemma (1,2,3) of Misra's draft book, Chapter 4, "Progress"*)
-Goal "[| leadsTo Acts A A';  id: Acts |] ==> \
-\      EX B. A<=B & leadsTo Acts B A' & constrains Acts (B-A') (B Un A')";
+Goal "[| leadsTo acts A A';  id: acts |] ==> \
+\      EX B. A<=B & leadsTo acts B A' & constrains acts (B-A') (B Un A')";
 by (etac leadsTo_induct 1);
 (*Basis*)
 by (blast_tac (claset() addIs [leadsTo_Basis]
@@ -458,10 +458,10 @@
 
 
 (*Misra's property W5*)
-Goal "id: Acts ==> constrains Acts (wlt Acts B - B) (wlt Acts B)";
+Goal "id: acts ==> constrains acts (wlt acts B - B) (wlt acts B)";
 by (forward_tac [wlt_leadsTo RS leadsTo_123] 1);
 by (Clarify_tac 1);
-by (subgoal_tac "Ba = wlt Acts B" 1);
+by (subgoal_tac "Ba = wlt acts B" 1);
 by (blast_tac (claset() addDs [leadsTo_eq_subset_wlt]) 2);
 by (Clarify_tac 1);
 by (asm_full_simp_tac (simpset() addsimps [wlt_increasing, Un_absorb2]) 1);
@@ -470,20 +470,20 @@
 
 (*** Completion: Binary and General Finite versions ***)
 
-Goal "[| leadsTo Acts A A';  stable Acts A';   \
-\      leadsTo Acts B B';  stable Acts B';  id: Acts |] \
-\   ==> leadsTo Acts (A Int B) (A' Int B')";
-by (subgoal_tac "stable Acts (wlt Acts B')" 1);
+Goal "[| leadsTo acts A A';  stable acts A';   \
+\      leadsTo acts B B';  stable acts B';  id: acts |] \
+\   ==> leadsTo acts (A Int B) (A' Int B')";
+by (subgoal_tac "stable acts (wlt acts B')" 1);
 by (asm_full_simp_tac (simpset() addsimps [stable_def]) 2);
 by (EVERY [etac (constrains_Un RS constrains_weaken) 2,
 	   etac wlt_constrains_wlt 2,
 	   fast_tac (claset() addEs [wlt_increasing RSN (2,rev_subsetD)]) 3,
 	   Blast_tac 2]);
-by (subgoal_tac "leadsTo Acts (A Int wlt Acts B') (A' Int wlt Acts B')" 1);
+by (subgoal_tac "leadsTo acts (A Int wlt acts B') (A' Int wlt acts B')" 1);
 by (blast_tac (claset() addIs [PSP_stable]) 2);
-by (subgoal_tac "leadsTo Acts (A' Int wlt Acts B') (A' Int B')" 1);
+by (subgoal_tac "leadsTo acts (A' Int wlt acts B') (A' Int B')" 1);
 by (blast_tac (claset() addIs [wlt_leadsTo, PSP_stable2]) 2);
-by (subgoal_tac "leadsTo Acts (A Int B) (A Int wlt Acts B')" 1);
+by (subgoal_tac "leadsTo acts (A Int B) (A Int wlt acts B')" 1);
 by (blast_tac (claset() addIs [leadsTo_subset RS subsetD, 
 			       subset_imp_leadsTo]) 2);
 (*Blast_tac gives PROOF FAILED*)
@@ -491,10 +491,10 @@
 qed "stable_completion";
 
 
-Goal "[| finite I;  id: Acts |]                     \
-\   ==> (ALL i:I. leadsTo Acts (A i) (A' i)) -->  \
-\       (ALL i:I. stable Acts (A' i)) -->         \
-\       leadsTo Acts (INT i:I. A i) (INT i:I. A' i)";
+Goal "[| finite I;  id: acts |]                     \
+\   ==> (ALL i:I. leadsTo acts (A i) (A' i)) -->  \
+\       (ALL i:I. stable acts (A' i)) -->         \
+\       leadsTo acts (INT i:I. A i) (INT i:I. A' i)";
 by (etac finite_induct 1);
 by (Asm_simp_tac 1);
 by (asm_simp_tac 
@@ -503,21 +503,21 @@
 qed_spec_mp "finite_stable_completion";
 
 
-Goal "[| W = wlt Acts (B' Un C);     \
-\      leadsTo Acts A (A' Un C);  constrains Acts A' (A' Un C);   \
-\      leadsTo Acts B (B' Un C);  constrains Acts B' (B' Un C);   \
-\      id: Acts |] \
-\   ==> leadsTo Acts (A Int B) ((A' Int B') Un C)";
-by (subgoal_tac "constrains Acts (W-C) (W Un B' Un C)" 1);
+Goal "[| W = wlt acts (B' Un C);     \
+\      leadsTo acts A (A' Un C);  constrains acts A' (A' Un C);   \
+\      leadsTo acts B (B' Un C);  constrains acts B' (B' Un C);   \
+\      id: acts |] \
+\   ==> leadsTo acts (A Int B) ((A' Int B') Un C)";
+by (subgoal_tac "constrains acts (W-C) (W Un B' Un C)" 1);
 by (blast_tac (claset() addIs [[asm_rl, wlt_constrains_wlt] 
 			       MRS constrains_Un RS constrains_weaken]) 2);
-by (subgoal_tac "constrains Acts (W-C) W" 1);
+by (subgoal_tac "constrains acts (W-C) W" 1);
 by (asm_full_simp_tac 
     (simpset() addsimps [wlt_increasing, Un_assoc, Un_absorb2]) 2);
-by (subgoal_tac "leadsTo Acts (A Int W - C) (A' Int W Un C)" 1);
+by (subgoal_tac "leadsTo acts (A Int W - C) (A' Int W Un C)" 1);
 by (simp_tac (simpset() addsimps [Int_Diff]) 2);
 by (blast_tac (claset() addIs [wlt_leadsTo, PSP RS leadsTo_weaken_R]) 2);
-by (subgoal_tac "leadsTo Acts (A' Int W Un C) (A' Int B' Un C)" 1);
+by (subgoal_tac "leadsTo acts (A' Int W Un C) (A' Int B' Un C)" 1);
 by (blast_tac (claset() addIs [wlt_leadsTo, leadsTo_Un_Un, 
                                PSP2 RS leadsTo_weaken_R, 
 			       subset_refl RS subset_imp_leadsTo, 
@@ -532,10 +532,10 @@
 bind_thm("completion", refl RS result());
 
 
-Goal "[| finite I;  id: Acts |] \
-\   ==> (ALL i:I. leadsTo Acts (A i) (A' i Un C)) -->  \
-\       (ALL i:I. constrains Acts (A' i) (A' i Un C)) --> \
-\       leadsTo Acts (INT i:I. A i) ((INT i:I. A' i) Un C)";
+Goal "[| finite I;  id: acts |] \
+\   ==> (ALL i:I. leadsTo acts (A i) (A' i Un C)) -->  \
+\       (ALL i:I. constrains acts (A' i) (A' i Un C)) --> \
+\       leadsTo acts (INT i:I. A i) ((INT i:I. A' i) Un C)";
 by (etac finite_induct 1);
 by (ALLGOALS Asm_simp_tac);
 by (Clarify_tac 1);
diff -r 1b0f14d11142 -r 82a5ca6290aa src/HOL/UNITY/WFair.thy
--- a/src/HOL/UNITY/WFair.thy	Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/WFair.thy	Wed Aug 05 10:57:25 1998 +0200
@@ -15,37 +15,37 @@
   (*This definition specifies weak fairness.  The rest of the theory
     is generic to all forms of fairness.*)
   transient :: "[('a * 'a)set set, 'a set] => bool"
-    "transient Acts A == EX act:Acts. A <= Domain act & act^^A <= Compl A"
+    "transient acts A == EX act:acts. A <= Domain act & act^^A <= Compl A"
 
   ensures :: "[('a * 'a)set set, 'a set, 'a set] => bool"
-    "ensures Acts A B == constrains Acts (A-B) (A Un B) & transient Acts (A-B)"
-			(*(unless Acts A B) would be equivalent*)
+    "ensures acts A B == constrains acts (A-B) (A Un B) & transient acts (A-B)"
+			(*(unless acts A B) would be equivalent*)
 
 consts leadsTo :: "[('a * 'a)set set, 'a set, 'a set] => bool"
        leadsto :: "[('a * 'a)set set] => ('a set * 'a set) set"
   
 translations
-  "leadsTo Acts A B" == "(A,B) : leadsto Acts"
+  "leadsTo acts A B" == "(A,B) : leadsto acts"
 
-inductive "leadsto Acts"
+inductive "leadsto acts"
   intrs 
 
-    Basis  "ensures Acts A B ==> leadsTo Acts A B"
+    Basis  "ensures acts A B ==> leadsTo acts A B"
 
-    Trans  "[| leadsTo Acts A B;  leadsTo Acts B C |]
-	   ==> leadsTo Acts A C"
+    Trans  "[| leadsTo acts A B;  leadsTo acts B C |]
+	   ==> leadsTo acts A C"
 
     (*Encoding using powerset of the desired axiom
-       (!!A. A : S ==> leadsTo Acts A B) ==> leadsTo Acts (Union S) B
+       (!!A. A : S ==> leadsTo acts A B) ==> leadsTo acts (Union S) B
     *)
-    Union  "(UN A:S. {(A,B)}) : Pow (leadsto Acts)
-	   ==> leadsTo Acts (Union S) B"
+    Union  "(UN A:S. {(A,B)}) : Pow (leadsto acts)
+	   ==> leadsTo acts (Union S) B"
 
   monos "[Pow_mono]"
 
 
-(*wlt Acts B is the largest set that leads to B*)
+(*wlt acts B is the largest set that leads to B*)
 constdefs wlt :: "[('a * 'a)set set, 'a set] => 'a set"
-  "wlt Acts B == Union {A. leadsTo Acts A B}"
+  "wlt acts B == Union {A. leadsTo acts A B}"
 
 end