src/HOL/UNITY/SubstAx.ML

 From Misra, "A Logic for Concurrent Programming", 1994
 *)
 
 open SubstAx;
 
-(*constrains Acts B B' ==> constrains Acts (reachable Init Acts Int B)
-                                           (reachable Init Acts Int B') *)
+(*constrains Acts B B' ==> constrains Acts (reachable(Init,Acts) Int B)
+                                           (reachable(Init,Acts) Int B') *)
 bind_thm ("constrains_reachable",
 	  rewrite_rule [stable_def] stable_reachable RS constrains_Int);
 
 
 (*** Introduction rules: Basis, Trans, Union ***)
 
-Goalw [LeadsTo_def]
-    "!!Acts. leadsTo Acts A B ==> LeadsTo Init Acts A B";
+Goal "leadsTo Acts A B ==> LeadsTo(Init,Acts) A B";
+by (simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (blast_tac (claset() addIs [PSP_stable2, stable_reachable]) 1);
 qed "leadsTo_imp_LeadsTo";
 
-Goalw [LeadsTo_def]
-    "!!Acts. [| constrains Acts (reachable Init Acts Int (A - A'))   \
+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'";
+\               transient  Acts (reachable(Init,Acts) Int (A-A')) |]   \
+\           ==> LeadsTo(Init,Acts) A A'";
+by (simp_tac (simpset() addsimps [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);
 qed "LeadsTo_Basis";
 
-Goalw [LeadsTo_def]
-    "!!Acts. [| LeadsTo Init Acts A B;  LeadsTo Init Acts B C |] \
-\            ==> LeadsTo Init Acts A C";
+Goal "[| LeadsTo(Init,Acts) A B;  LeadsTo(Init,Acts) B C |] \
+\            ==> LeadsTo(Init,Acts) A C";
+by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (blast_tac (claset() addIs [leadsTo_Trans]) 1);
 qed "LeadsTo_Trans";
 
-val prems = goalw thy [LeadsTo_def]
- "(!!A. A : S ==> LeadsTo Init Acts A B) ==> LeadsTo Init Acts (Union S) B";
+val [prem] = goalw thy [LeadsTo_def]
+ "(!!A. A : S ==> LeadsTo(Init,Acts) A B) ==> LeadsTo(Init,Acts) (Union S) B";
+by (Simp_tac 1);
 by (stac Int_Union 1);
-by (blast_tac (claset() addIs (leadsTo_UN::prems)) 1);
+by (blast_tac (claset() addIs [leadsTo_UN,
+			        simplify (simpset()) prem]) 1);
 qed "LeadsTo_Union";
 
 
 (*** Derived rules ***)
 
-Goal "!!Acts. id: Acts ==> LeadsTo Init Acts A UNIV";
+Goal "id: Acts ==> LeadsTo(Init,Acts) 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 "!!Acts. LeadsTo Init Acts A (A' Un A') ==> LeadsTo Init Acts A A'";
+Goal "LeadsTo(Init,Acts) A (A' Un A') ==> LeadsTo(Init,Acts) A A'";
 by (asm_full_simp_tac (simpset() addsimps Un_ac) 1);
 qed "LeadsTo_Un_duplicate";
 
-Goal "!!Acts. LeadsTo Init Acts A (A' Un C Un C) ==> LeadsTo Init Acts A (A' Un C)";
+Goal "LeadsTo(Init,Acts) A (A' Un C Un C) ==> LeadsTo(Init,Acts) 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(Init,Acts) (A i) B) \
+\   ==> LeadsTo(Init,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
-  "!!C. [| LeadsTo Init Acts A C; LeadsTo Init Acts B C |] ==> LeadsTo Init Acts (A Un B) C";
+  "[| LeadsTo(Init,Acts) A C; LeadsTo(Init,Acts) B C |] ==> LeadsTo(Init,Acts) (A Un B) C";
 by (stac Un_eq_Union 1);
 by (blast_tac (claset() addIs [LeadsTo_Union]) 1);
 qed "LeadsTo_Un";
 
 
-Goalw [LeadsTo_def]
-    "!!A B. [| reachable Init Acts Int A <= B;  id: Acts |] \
-\           ==> LeadsTo Init Acts A B";
+Goal "[| reachable(Init,Acts) Int A <= B;  id: Acts |] \
+\            ==> LeadsTo(Init,Acts) A B";
+by (simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (blast_tac (claset() addIs [subset_imp_leadsTo]) 1);
 qed "Int_subset_imp_LeadsTo";
 
-Goalw [LeadsTo_def]
-    "!!A B. [| A <= B;  id: Acts |] \
-\           ==> LeadsTo Init Acts A B";
+Goal "[| A <= B;  id: Acts |] ==> LeadsTo(Init,Acts) A B";
+by (simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (blast_tac (claset() addIs [subset_imp_leadsTo]) 1);
 qed "subset_imp_LeadsTo";
 
 bind_thm ("empty_LeadsTo", empty_subsetI RS subset_imp_LeadsTo);
 Addsimps [empty_LeadsTo];
 
-Goal
-    "!!A B. [| reachable Init Acts Int A = {};  id: Acts |] \
-\           ==> LeadsTo Init Acts A B";
+Goal "[| reachable(Init,Acts) Int A = {};  id: Acts |] \
+\            ==> LeadsTo(Init,Acts) A B";
 by (asm_simp_tac (simpset() addsimps [Int_subset_imp_LeadsTo]) 1);
 qed "Int_empty_LeadsTo";
 
 
-Goalw [LeadsTo_def]
-    "!!Acts. [| LeadsTo Init Acts A A';   \
-\               reachable Init Acts Int A' <= B' |] \
-\            ==> LeadsTo Init Acts A B'";
+Goal "[| LeadsTo(Init,Acts) A A';   \
+\                reachable(Init,Acts) Int A' <= B' |] \
+\             ==> LeadsTo(Init,Acts) 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";
 
 
-Goalw [LeadsTo_def]
-    "!!Acts. [| LeadsTo Init Acts A A'; \
-     \               reachable Init Acts Int B <= A; id: Acts |]  \
-\            ==> LeadsTo Init Acts B A'";
+Goal "[| LeadsTo(Init,Acts) A A'; \
+\                reachable(Init,Acts) Int B <= A; id: Acts |]  \
+\             ==> LeadsTo(Init,Acts) 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
-  "!!C. id: Acts ==> \
-\       LeadsTo Init Acts (A Un B) C  =  \
-\       (LeadsTo Init Acts A C & LeadsTo Init Acts B C)";
+  "id: Acts ==> \
+\       LeadsTo(Init,Acts) (A Un B) C  =  \
+\       (LeadsTo(Init,Acts) A C & LeadsTo(Init,Acts) B C)";
 by (blast_tac (claset() addIs [LeadsTo_Un, LeadsTo_weaken_L]) 1);
 qed "LeadsTo_Un_distrib";
 
 Goal
-  "!!C. id: Acts ==> \
-\       LeadsTo Init Acts (UN i:I. A i) B  =  \
-\       (ALL i : I. LeadsTo Init Acts (A i) B)";
+  "id: Acts ==> \
+\       LeadsTo(Init,Acts) (UN i:I. A i) B  =  \
+\       (ALL i : I. LeadsTo(Init,Acts) (A i) B)";
 by (blast_tac (claset() addIs [LeadsTo_UN, LeadsTo_weaken_L]) 1);
 qed "LeadsTo_UN_distrib";
 
 Goal
-  "!!C. id: Acts ==> \
-\       LeadsTo Init Acts (Union S) B  =  \
-\       (ALL A : S. LeadsTo Init Acts A B)";
+  "id: Acts ==> \
+\       LeadsTo(Init,Acts) (Union S) B  =  \
+\       (ALL A : S. LeadsTo(Init,Acts) A B)";
 by (blast_tac (claset() addIs [LeadsTo_Union, LeadsTo_weaken_L]) 1);
 qed "LeadsTo_Union_distrib";
 
 
 Goal 
-   "!!Acts. [| LeadsTo Init Acts A A'; id: Acts;   \
-\               reachable Init Acts Int B  <= A;     \
-\               reachable Init Acts Int A' <= B' |] \
-\           ==> LeadsTo Init Acts B B'";
+   "[| LeadsTo(Init,Acts) A A'; id: Acts;   \
+\               reachable(Init,Acts) Int B  <= A;     \
+\               reachable(Init,Acts) Int A' <= B' |] \
+\           ==> LeadsTo(Init,Acts) 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
-  "!!C. [| LeadsTo Init Acts (A-B) C; LeadsTo Init Acts B C; id: Acts |] \
-\       ==> LeadsTo Init Acts A C";
+  "[| LeadsTo(Init,Acts) (A-B) C; LeadsTo(Init,Acts) B C; id: Acts |] \
+\       ==> LeadsTo(Init,Acts) A C";
 by (blast_tac (claset() addIs [LeadsTo_Un, LeadsTo_weaken]) 1);
 qed "LeadsTo_Diff";
 
 
 (** Meta or object quantifier ???????????????????
     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(Init,Acts) (A i) (A' i)) \
+\   ==> LeadsTo(Init,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);
 qed "LeadsTo_UN_UN";
 
 
 (*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(Init,Acts) (A i) (A' i)) \
+\   ==> LeadsTo(Init,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
-   "!!Acts. ALL i. LeadsTo Init Acts (A i) (A' i) \
-\           ==> LeadsTo Init Acts (UN i. A i) (UN i. A' i)";
+   "ALL i. LeadsTo(Init,Acts) (A i) (A' i) \
+\           ==> LeadsTo(Init,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 "!!Acts. [| LeadsTo Init Acts A A'; LeadsTo Init Acts B B' |] \
-\                 ==> LeadsTo Init Acts (A Un B) (A' Un B')";
+Goal "[| LeadsTo(Init,Acts) A A'; LeadsTo(Init,Acts) B B' |] \
+\                 ==> LeadsTo(Init,Acts) (A Un B) (A' Un B')";
 by (blast_tac (claset() addIs [LeadsTo_Un, 
 			       LeadsTo_weaken_R]) 1);
 qed "LeadsTo_Un_Un";
 
 
 (** The cancellation law **)
 
 Goal
-   "!!Acts. [| LeadsTo Init Acts A (A' Un B); LeadsTo Init Acts B B'; \
+   "[| LeadsTo(Init,Acts) A (A' Un B); LeadsTo(Init,Acts) B B'; \
 \              id: Acts |]    \
-\           ==> LeadsTo Init Acts A (A' Un B')";
+\           ==> LeadsTo(Init,Acts) A (A' Un B')";
 by (blast_tac (claset() addIs [LeadsTo_Un_Un, 
 			       subset_imp_LeadsTo, LeadsTo_Trans]) 1);
 qed "LeadsTo_cancel2";
 
 Goal
-   "!!Acts. [| LeadsTo Init Acts A (A' Un B); LeadsTo Init Acts (B-A') B'; id: Acts |] \
-\           ==> LeadsTo Init Acts A (A' Un B')";
+   "[| LeadsTo(Init,Acts) A (A' Un B); LeadsTo(Init,Acts) (B-A') B'; id: Acts |] \
+\           ==> LeadsTo(Init,Acts) A (A' Un B')";
 by (rtac LeadsTo_cancel2 1);
 by (assume_tac 2);
 by (ALLGOALS Asm_simp_tac);
 qed "LeadsTo_cancel_Diff2";
 
 Goal
-   "!!Acts. [| LeadsTo Init Acts A (B Un A'); LeadsTo Init Acts B B'; id: Acts |] \
-\           ==> LeadsTo Init Acts A (B' Un A')";
+   "[| LeadsTo(Init,Acts) A (B Un A'); LeadsTo(Init,Acts) B B'; id: Acts |] \
+\           ==> LeadsTo(Init,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
-   "!!Acts. [| LeadsTo Init Acts A (B Un A'); LeadsTo Init Acts (B-A') B'; id: Acts |] \
-\           ==> LeadsTo Init Acts A (B' Un A')";
+   "[| LeadsTo(Init,Acts) A (B Un A'); LeadsTo(Init,Acts) (B-A') B'; id: Acts |] \
+\           ==> LeadsTo(Init,Acts) A (B' Un A')";
 by (rtac LeadsTo_cancel1 1);
 by (assume_tac 2);
 by (ALLGOALS Asm_simp_tac);
 qed "LeadsTo_cancel_Diff1";
 
 
 
 (** The impossibility law **)
 
-Goalw [LeadsTo_def]
-    "!!Acts. LeadsTo Init Acts A {} ==> reachable Init Acts Int A  = {}";
-by (Full_simp_tac 1);
+Goal "LeadsTo(Init,Acts) A {} ==> reachable(Init,Acts) Int A  = {}";
+by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (etac leadsTo_empty 1);
 qed "LeadsTo_empty";
 
 
 (** PSP: Progress-Safety-Progress **)
 
 (*Special case of PSP: Misra's "stable conjunction".  Doesn't need id:Acts. *)
-Goalw [LeadsTo_def]
-   "!!Acts. [| LeadsTo Init Acts A A'; stable Acts B |] \
-\           ==> LeadsTo Init Acts (A Int B) (A' Int B)";
-by (asm_simp_tac (simpset() addsimps [Int_assoc RS sym, PSP_stable]) 1);
+Goal "[| LeadsTo(Init,Acts) A A'; stable Acts B |] \
+\           ==> LeadsTo(Init,Acts) (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
-   "!!Acts. [| LeadsTo Init Acts A A'; stable Acts B |] \
-\           ==> LeadsTo Init Acts (B Int A) (B Int A')";
+Goal "[| LeadsTo(Init,Acts) A A'; stable Acts B |] \
+\             ==> LeadsTo(Init,Acts) (B Int A) (B Int A')";
 by (asm_simp_tac (simpset() addsimps (R_PSP_stable::Int_ac)) 1);
 qed "R_PSP_stable2";
 
 
-Goalw [LeadsTo_def]
-   "!!Acts. [| 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(Init,Acts) A A'; constrains Acts B B'; id: Acts |] \
+\           ==> LeadsTo(Init,Acts) (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);
 by (etac leadsTo_weaken 2);
 by (ALLGOALS Blast_tac);
 qed "R_PSP";
 
 Goal
-   "!!Acts. [| LeadsTo Init Acts A A'; constrains Acts B B'; id: Acts |] \
-\           ==> LeadsTo Init Acts (B Int A) ((B Int A') Un (B' - B))";
+   "[| LeadsTo(Init,Acts) A A'; constrains Acts B B'; id: Acts |] \
+\           ==> LeadsTo(Init,Acts) (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]
-   "!!Acts. [| LeadsTo Init Acts A A'; unless Acts B B'; id: Acts |] \
-\           ==> LeadsTo Init Acts (A Int B) ((A' Int B) Un B')";
+   "[| LeadsTo(Init,Acts) A A'; unless Acts B B'; id: Acts |] \
+\           ==> LeadsTo(Init,Acts) (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);
 by (asm_full_simp_tac (simpset() addsimps [Diff_Int_distrib]) 2);
 by (etac LeadsTo_Diff 2);

 
 
 (*** Induction rules ***)
 
 (** Meta or object quantifier ????? **)
-Goalw [LeadsTo_def]
-   "!!Acts. [| wf r;     \
-\              ALL m. LeadsTo Init Acts (A Int f-``{m})                     \
+Goal
+   "[| wf r;     \
+\              ALL m. LeadsTo(Init,Acts) (A Int f-``{m})                     \
 \                                       ((A Int f-``(r^-1 ^^ {m})) Un B);   \
 \              id: Acts |] \
-\           ==> LeadsTo Init Acts A B";
+\           ==> LeadsTo(Init,Acts) A B";
+by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1);
 by (etac leadsTo_wf_induct 1);
 by (assume_tac 2);
 by (blast_tac (claset() addIs [leadsTo_weaken]) 1);
 qed "LeadsTo_wf_induct";
 
 
 Goal
-   "!!Acts. [| wf r;     \
-\              ALL m:I. LeadsTo Init Acts (A Int f-``{m})                   \
+   "[| wf r;     \
+\              ALL m:I. LeadsTo(Init,Acts) (A Int f-``{m})                   \
 \                                  ((A Int f-``(r^-1 ^^ {m})) Un B);   \
 \              id: Acts |] \
-\           ==> LeadsTo Init Acts A ((A - (f-``I)) Un B)";
+\           ==> LeadsTo(Init,Acts) A ((A - (f-``I)) Un B)";
 by (etac LeadsTo_wf_induct 1);
 by Safe_tac;
 by (case_tac "m:I" 1);
 by (blast_tac (claset() addIs [LeadsTo_weaken]) 1);
 by (blast_tac (claset() addIs [subset_imp_LeadsTo]) 1);
 qed "R_bounded_induct";
 
 
 Goal
-   "!!Acts. [| ALL m. LeadsTo Init Acts (A Int f-``{m})                     \
+   "[| ALL m. LeadsTo(Init,Acts) (A Int f-``{m})                     \
 \                                  ((A Int f-``(lessThan m)) Un B);   \
 \              id: Acts |] \
-\           ==> LeadsTo Init Acts A B";
+\           ==> LeadsTo(Init,Acts) 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
-   "!!Acts. [| ALL m:(greaterThan l). LeadsTo Init Acts (A Int f-``{m})   \
+   "[| ALL m:(greaterThan l). LeadsTo(Init,Acts) (A Int f-``{m})   \
 \                                        ((A Int f-``(lessThan m)) Un B);   \
 \              id: Acts |] \
-\           ==> LeadsTo Init Acts A ((A Int (f-``(atMost l))) Un B)";
+\           ==> LeadsTo(Init,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 R_bounded_induct) 1);
 by (assume_tac 2);
 by (Asm_simp_tac 1);
 qed "R_lessThan_bounded_induct";
 
 Goal
-   "!!Acts. [| ALL m:(lessThan l). LeadsTo Init Acts (A Int f-``{m})   \
+   "[| ALL m:(lessThan l). LeadsTo(Init,Acts) (A Int f-``{m})   \
 \                                    ((A Int f-``(greaterThan m)) Un B);   \
 \              id: Acts |] \
-\           ==> LeadsTo Init Acts A ((A Int (f-``(atLeast l))) Un B)";
+\           ==> LeadsTo(Init,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);
 by (simp_tac (simpset() addsimps [inv_image_def, Image_singleton]) 1);
 by (Clarify_tac 1);

 
 
 
 (*** Completion: Binary and General Finite versions ***)
 
-Goalw [LeadsTo_def]
-   "!!Acts. [| 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(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')";
+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
-   "!!Acts. [| finite I;  id: Acts |]                     \
-\           ==> (ALL i:I. LeadsTo Init Acts (A i) (A' i)) -->  \
+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)";
+\               LeadsTo(Init,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 
     (simpset() addsimps [R_stable_completion, stable_def, 
 			 ball_constrains_INT]) 1);
 qed_spec_mp "R_finite_stable_completion";
 
 
-Goalw [LeadsTo_def]
- "!!Acts. [| 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); \
+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)";
-
-by (full_simp_tac (simpset() addsimps [Int_Un_distrib]) 1);
+\         ==> LeadsTo(Init,Acts) (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);
 by (ALLGOALS 
     (asm_simp_tac 
      (simpset() addsimps [constrains_reachable, Int_Un_distrib RS sym])));
 by (blast_tac (claset() addIs [leadsTo_weaken]) 1);
 qed "R_completion";
 
 
 Goal
-   "!!Acts. [| finite I;  id: Acts |] \
-\           ==> (ALL i:I. LeadsTo Init Acts (A i) (A' i Un C)) -->  \
+   "[| 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)";
+\               LeadsTo(Init,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);
 by (dtac ball_constrains_INT 1);
 by (asm_full_simp_tac (simpset() addsimps [R_completion]) 1);