Tidied up some proofs

--- a/src/HOL/MiniML/I.ML	Mon Oct 07 10:31:50 1996 +0200
+++ b/src/HOL/MiniML/I.ML	Mon Oct 07 10:34:58 1996 +0200
@@ -9,7 +9,6 @@
   (* case Var n *)
   by (simp_tac (!simpset addsimps [app_subst_list]
       setloop (split_inside_tac [expand_if])) 1);
-  by (fast_tac (HOL_cs addss !simpset) 1);
 
  (* case Abs e *)
  by (asm_full_simp_tac (!simpset setloop (split_inside_tac [expand_bind])) 1);
@@ -21,14 +20,14 @@
    by (fast_tac (HOL_cs addss (!simpset addsimps [new_tv_subst])) 2);
   by (fast_tac (HOL_cs addIs [new_tv_Suc_list RS mp,new_tv_subst_le,
                               less_imp_le,lessI]) 1); 
-
+(** LEVEL 10 **)
  by (strip_tac 1);
  by (REPEAT (etac allE 1));
  by (etac impE 1);
   by (fast_tac (HOL_cs addss (!simpset addsimps [new_tv_subst])) 2);
  by (fast_tac (HOL_cs addIs [new_tv_Suc_list RS mp,new_tv_subst_le,
                              less_imp_le,lessI]) 1);
-
+(** LEVEL 15 **)
 (* case App e1 e2 *)
 by (simp_tac (!simpset setloop (split_inside_tac [expand_bind])) 1);
 by (strip_tac 1);
@@ -49,6 +48,7 @@
 by (eres_inst_tac [("x","s2'")] allE 1);
 by (eres_inst_tac [("x","t2")] allE 1);
 by (eres_inst_tac [("x","n2")] allE 1);
+(** LEVEL 34 **)
 by (rtac conjI 1);
  by (strip_tac 1);
  by (mp_tac 1);
@@ -61,6 +61,7 @@
   by (fast_tac (HOL_cs addDs [sym RS W_var_geD,new_tv_subst_le,new_tv_list_le] 
                        addss !simpset) 1);
  by (fast_tac (HOL_cs addss (!simpset addsimps [subst_comp_tel])) 1);
+(** LEVEL 45 **)
 by (strip_tac 1);
 by (rename_tac "s2 t2' n2'" 1);
 by (rtac conjI 1);
@@ -77,6 +78,7 @@
  by (fast_tac (HOL_cs addss (!simpset addsimps [subst_comp_tel,subst_comp_te])) 1);
 by (strip_tac 1);
 by (mp_tac 1);
+(** LEVEL 60 **)
 by (mp_tac 1);
 by (etac exE 1);
 by (etac conjE 1);
@@ -90,25 +92,26 @@
 by (REPEAT(EVERY1
      [asm_full_simp_tac (!simpset addsimps [subst_comp_tel,subst_comp_te]),
       REPEAT o etac conjE, hyp_subst_tac]));
-by (rtac exI 1);
+(** LEVEL 70 **)
 by (safe_tac HOL_cs);
-  by (fast_tac HOL_cs 1);
  by (simp_tac (!simpset addsimps [o_def,subst_comp_te]) 2);
 by (subgoal_tac "new_tv n2 s & new_tv n2 r & new_tv n2 ra" 1);
  by (asm_full_simp_tac (!simpset addsimps [new_tv_subst]) 1);
 by ((forward_tac [new_tv_subst_tel] 1) THEN (atac 1));
 by ((dres_inst_tac [("a","$ s a")] new_tv_W 1) THEN (atac 1));
 by (safe_tac HOL_cs);
-  by (fast_tac (HOL_cs addDs[sym RS W_var_geD,new_tv_subst_le,new_tv_list_le] 
+  by (best_tac (HOL_cs addDs[sym RS W_var_geD,new_tv_subst_le,new_tv_list_le] 
                        addss !simpset) 1);
  by (fast_tac (HOL_cs addDs [sym RS W_var_geD,new_tv_subst_le,new_tv_list_le] 
                       addss !simpset) 1);
+(** LEVEL 79 **)
 by (dres_inst_tac [("e","expr1")] (sym RS W_var_geD) 1);
 by ((dtac new_tv_subst_tel 1) THEN (atac 1));
 by ((dres_inst_tac [("ts","$ s a")] new_tv_list_le 1) THEN (atac 1));
 by ((dtac new_tv_subst_tel 1) THEN (atac 1));
-by (fast_tac (HOL_cs addDs [new_tv_W] addss 
-    (!simpset addsimps [subst_comp_tel])) 1);
+by (best_tac (HOL_cs addDs [new_tv_W] 
+                     addss (!simpset addsimps [subst_comp_tel])) 1);
+(** LEVEL 84 **)
 qed_spec_mp "I_correct_wrt_W";
 
 (***
@@ -133,22 +136,23 @@
 goal I.thy "!a m s. \
 \  new_tv m a & new_tv m s --> I e a m s = Fail --> W e ($s a) m = Fail";
 by (expr.induct_tac "e" 1);
-  by(simp_tac (!simpset addsimps [app_subst_list]
+  by (simp_tac (!simpset addsimps [app_subst_list]
                         setloop (split_tac [expand_if])) 1);
- by(Simp_tac 1);
- by(strip_tac 1);
- br conjI 1;
-  by(strip_tac 1);
-  by(subgoal_tac "TVar m # $ s a = $s(TVar m # a)" 1);
-   by(asm_simp_tac (HOL_ss addsimps
+ by (Simp_tac 1);
+ by (strip_tac 1);
+ by (rtac conjI 1);
+  by (strip_tac 1);
+  by (subgoal_tac "TVar m # $ s a = $s(TVar m # a)" 1);
+   by (asm_simp_tac (HOL_ss addsimps
         [new_tv_Suc_list, lessI RS less_imp_le RS new_tv_subst_le]) 1);
-  be conjE 1;
-  bd (new_tv_not_free_tv RS not_free_impl_id) 1;
-  by(Asm_simp_tac 1);
- by(strip_tac 1);
- be exE 1;
- by(split_all_tac 1);
- by(Full_simp_tac 1);
+  by (etac conjE 1);
+  by (dtac (new_tv_not_free_tv RS not_free_impl_id) 1);
+  by (Asm_simp_tac 1);
+ by (strip_tac 1);
+ by (etac exE 1);
+ by (split_all_tac 1);
+ by (Full_simp_tac 1);
+(** LEVEL 15 **)
 by (Asm_simp_tac 1);
 by (strip_tac 1);
 by (etac exE 1);
@@ -156,43 +160,41 @@
 by (split_all_tac 1);
 by (Full_simp_tac 1);
 by (dtac lemma 1);
- by(fast_tac HOL_cs 1);
+ by (fast_tac HOL_cs 1);
+(** LEVEL 23 **)
 by (etac exE 1);
 by (etac conjE 1);
 by (hyp_subst_tac 1);
 by (Asm_simp_tac 1);
-by (rtac exI 1);
-by (rtac conjI 1);
- br refl 1;
-by (Simp_tac 1);
 by (etac disjE 1);
- br disjI1 1;
- by(full_simp_tac (!simpset addsimps [o_def,subst_comp_tel]) 1);
- by(EVERY[etac allE 1, etac allE 1, etac allE 1,
+ by (rtac disjI1 1);
+(** LEVEL 29 **)
+ by (full_simp_tac (!simpset addsimps [o_def,subst_comp_tel]) 1);
+ by (EVERY[etac allE 1, etac allE 1, etac allE 1,
           etac impE 1, etac impE 2, atac 2, atac 2]);
- br conjI 1;
-  by(fast_tac (HOL_cs addIs [W_var_ge RS new_tv_list_le]) 1);
- br new_tv_subst_comp_2 1;
-  by(fast_tac (HOL_cs addIs [W_var_ge RS new_tv_subst_le]) 1);
- by(fast_tac (HOL_cs addSIs [new_tv_subst_tel]addIs[new_tv_W RS conjunct1])1);
+ by (rtac conjI 1);
+  by (fast_tac (HOL_cs addIs [W_var_ge RS new_tv_list_le]) 1);
+ by (rtac new_tv_subst_comp_2 1);
+  by (fast_tac (HOL_cs addIs [W_var_ge RS new_tv_subst_le]) 1);
+ by (fast_tac (HOL_cs addSIs [new_tv_subst_tel]addIs[new_tv_W RS conjunct1])1);
 by (rtac disjI2 1);
 by (etac exE 1);
 by (split_all_tac 1);
 by (etac conjE 1);
+(** LEVEL 40 **)
 by (Full_simp_tac 1);
 by (dtac lemma 1);
- br conjI 1;
-  by(fast_tac (HOL_cs addIs [W_var_ge RS new_tv_list_le]) 1);
- br new_tv_subst_comp_1 1;
-   by(fast_tac (HOL_cs addIs [W_var_ge RS new_tv_subst_le]) 1);
- by(fast_tac (HOL_cs addSIs [new_tv_subst_tel]addIs[new_tv_W RS conjunct1])1);
+ by (rtac conjI 1);
+  by (fast_tac (HOL_cs addIs [W_var_ge RS new_tv_list_le]) 1);
+ by (rtac new_tv_subst_comp_1 1);
+   by (fast_tac (HOL_cs addIs [W_var_ge RS new_tv_subst_le]) 1);
+ by (fast_tac (HOL_cs addSIs [new_tv_subst_tel]addIs[new_tv_W RS conjunct1])1);
 by (etac exE 1);
 by (etac conjE 1);
 by (hyp_subst_tac 1);
+(** LEVEL 50 **)
 by (asm_full_simp_tac (!simpset addsimps
      [o_def,subst_comp_te RS sym,subst_comp_tel RS sym]) 1);
-by (asm_simp_tac (!simpset addcongs [conj_cong] addsimps
-           [eq_sym_conv,subst_comp_te RS sym,subst_comp_tel RS sym]) 1);
 qed_spec_mp "I_complete_wrt_W";
 
 (***

--- a/src/HOL/MiniML/Maybe.ML	Mon Oct 07 10:31:50 1996 +0200
+++ b/src/HOL/MiniML/Maybe.ML	Mon Oct 07 10:34:58 1996 +0200
@@ -22,7 +22,6 @@
 goal Maybe.thy
   "((m bind f) = Fail) = ((m=Fail) | (? p. m = Ok p & f p = Fail))";
 by (simp_tac (!simpset setloop (split_tac [expand_bind])) 1);
-by (fast_tac HOL_cs 1);
 qed "bind_eq_Fail";
 
 Addsimps [bind_eq_Fail];

--- a/src/HOL/MiniML/W.ML	Mon Oct 07 10:31:50 1996 +0200
+++ b/src/HOL/MiniML/W.ML	Mon Oct 07 10:34:58 1996 +0200
@@ -235,6 +235,7 @@
 by (res_inst_tac [("x","s'")] exI 1);
 by (Asm_simp_tac 1);
 
+(** LEVEL 10 **)
 (* case Abs e *)
 by (strip_tac 1);
 by (eresolve_tac has_type_casesE 1);
@@ -245,6 +246,7 @@
 by (fast_tac (HOL_cs addss (!simpset addcongs [conj_cong]
                             setloop (split_tac [expand_bind]))) 1);
 
+(** LEVEL 17 **)
 (* case App e1 e2 *)
 by (strip_tac 1);
 by (eresolve_tac has_type_casesE 1);
@@ -266,6 +268,7 @@
 by (fast_tac (HOL_cs addIs [sym RS W_var_geD,new_tv_W RS
                             conjunct1,new_tv_list_le,new_tv_subst_tel]) 1);
 
+(** LEVEL 35 **)
 by (subgoal_tac
   "$ (%x.if x=ma then t' else (if x:(free_tv t - free_tv sa) then r x \
 \        else ra x)) ($ sa t) = \
@@ -280,6 +283,7 @@
 by (subgoal_tac "na ~=ma" 2);
 by (fast_tac (HOL_cs addDs [new_tv_W,sym RS W_var_geD,
                             new_tv_not_free_tv,new_tv_le]) 3);
+(** LEVEL 42 **)
 by (case_tac "na:free_tv sa" 2);
 (* na ~: free_tv sa *)
 by (asm_simp_tac (!simpset addsimps [not_free_impl_id]
@@ -293,6 +297,7 @@
 (* na ~: dom sa *)
 by (asm_full_simp_tac (!simpset addsimps [dom_def] 
                        setloop (split_tac [expand_if])) 3);
+(** LEVEL 50 **)
 (* na : dom sa *)
 by (rtac eq_free_eq_subst_te 2);
 by (strip_tac 2);
@@ -307,6 +312,7 @@
                             setloop (split_tac [expand_if]))) 2);
 
 by (Simp_tac 2);  
+(** LEVEL 60 **)
 by (rtac eq_free_eq_subst_te 2);
 by (strip_tac 2 );
 by (subgoal_tac "na ~= ma" 2);
@@ -315,6 +321,7 @@
 by (dtac (sym RS W_var_geD) 3);
 by (fast_tac (HOL_cs addDs [new_tv_list_le,new_tv_subst_tel,new_tv_W,new_tv_not_free_tv]) 3);
 by (case_tac "na: free_tv t - free_tv sa" 2);
+(** LEVEL 68 **)
 (* case na ~: free_tv t - free_tv sa *)
 by ( asm_full_simp_tac (!simpset setloop (split_tac [expand_if])) 3);
 (* case na : free_tv t - free_tv sa *)