src/HOL/MiniML/I.ML
author nipkow
Fri, 17 Jan 1997 18:32:24 +0100
changeset 2523 0ccea141409b
parent 2058 ff04984186e9
permissions -rw-r--r--
Updated documentation pointers.
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open I;
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goal thy
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  "! a m s s' t n.  \
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\    (new_tv m a & new_tv m s) --> I e a m s = Ok(s',t,n) -->   \
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\    ( ? r. W e ($ s a) m = Ok(r, $ s' t, n) & s' = ($ r o s) )";
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by (expr.induct_tac "e" 1);
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  (* case Var n *)
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  by (simp_tac (!simpset addsimps [app_subst_list]
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      setloop (split_inside_tac [expand_if])) 1);
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 (* case Abs e *)
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 by (asm_full_simp_tac (!simpset setloop (split_inside_tac [expand_bind])) 1);
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 by (strip_tac 1);
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 by (rtac conjI 1);
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  by (strip_tac 1);
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  by (REPEAT (etac allE 1));
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  by (etac impE 1);
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   by (fast_tac (HOL_cs addss (!simpset addsimps [new_tv_subst])) 2);
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  by (fast_tac (HOL_cs addIs [new_tv_Suc_list RS mp,new_tv_subst_le,
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                              less_imp_le,lessI]) 1); 
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(** LEVEL 10 **)
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 by (strip_tac 1);
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 by (REPEAT (etac allE 1));
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 by (etac impE 1);
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  by (fast_tac (HOL_cs addss (!simpset addsimps [new_tv_subst])) 2);
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 by (fast_tac (HOL_cs addIs [new_tv_Suc_list RS mp,new_tv_subst_le,
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                             less_imp_le,lessI]) 1);
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(** LEVEL 15 **)
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(* case App e1 e2 *)
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by (simp_tac (!simpset setloop (split_inside_tac [expand_bind])) 1);
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by (strip_tac 1);
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by (rename_tac "s1' t1 n1 s2' t2 n2 sa" 1);
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by (rtac conjI 1);
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 by (fast_tac (HOL_cs addss !simpset) 1);
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by (strip_tac 1);
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by (rename_tac "s1 t1' n1'" 1);
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by (eres_inst_tac [("x","a")] allE 1);
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by (eres_inst_tac [("x","m")] allE 1);
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by (eres_inst_tac [("x","s")] allE 1);
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by (eres_inst_tac [("x","s1'")] allE 1);
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by (eres_inst_tac [("x","t1")] allE 1);
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by (eres_inst_tac [("x","n1")] allE 1);
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by (eres_inst_tac [("x","a")] allE 1);
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by (eres_inst_tac [("x","n1")] allE 1);
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by (eres_inst_tac [("x","s1'")] allE 1);
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by (eres_inst_tac [("x","s2'")] allE 1);
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by (eres_inst_tac [("x","t2")] allE 1);
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by (eres_inst_tac [("x","n2")] allE 1);
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(** LEVEL 34 **)
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by (rtac conjI 1);
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 by (strip_tac 1);
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 by (mp_tac 1);
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 by (mp_tac 1);
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 by (etac exE 1);
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 by (etac conjE 1);
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 by (etac impE 1);
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  by ((forward_tac [new_tv_subst_tel] 1) THEN (atac 1)); 
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  by ((dres_inst_tac [("a","$ s a")] new_tv_W 1) THEN (atac 1));
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  by (fast_tac (HOL_cs addDs [sym RS W_var_geD,new_tv_subst_le,new_tv_list_le] 
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                       addss !simpset) 1);
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 by (fast_tac (HOL_cs addss (!simpset addsimps [subst_comp_tel])) 1);
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(** LEVEL 45 **)
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by (strip_tac 1);
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by (rename_tac "s2 t2' n2'" 1);
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by (rtac conjI 1);
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 by (strip_tac 1);
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 by (mp_tac 1);
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 by (mp_tac 1);
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 by (etac exE 1);
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 by (etac conjE 1);
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 by (etac impE 1);
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  by ((forward_tac [new_tv_subst_tel] 1) THEN (atac 1)); 
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  by ((dres_inst_tac [("a","$ s a")] new_tv_W 1) THEN (atac 1));
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  by (fast_tac (HOL_cs addDs [sym RS W_var_geD,new_tv_subst_le,new_tv_list_le] 
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                       addss !simpset) 1);
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 by (fast_tac (HOL_cs addss (!simpset addsimps [subst_comp_tel,subst_comp_te])) 1);
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by (strip_tac 1);
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by (mp_tac 1);
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(** LEVEL 60 **)
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by (mp_tac 1);
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by (etac exE 1);
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by (etac conjE 1);
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by (etac impE 1);
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 by ((forward_tac [new_tv_subst_tel] 1) THEN (atac 1)); 
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 by ((dres_inst_tac [("a","$ s a")] new_tv_W 1) THEN (atac 1));
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 by (fast_tac (HOL_cs addDs [sym RS W_var_geD,new_tv_subst_le,new_tv_list_le] 
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                      addss !simpset) 1);
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by (mp_tac 1);
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by (REPEAT (eresolve_tac [exE,conjE] 1));
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by (REPEAT(EVERY1
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     [asm_full_simp_tac (!simpset addsimps [subst_comp_tel,subst_comp_te]),
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      REPEAT o etac conjE, hyp_subst_tac]));
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(** LEVEL 70 **)
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by (safe_tac HOL_cs);
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 by (simp_tac (!simpset addsimps [o_def,subst_comp_te]) 2);
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by (subgoal_tac "new_tv n2 s & new_tv n2 r & new_tv n2 ra" 1);
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 by (asm_full_simp_tac (!simpset addsimps [new_tv_subst]) 1);
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by ((forward_tac [new_tv_subst_tel] 1) THEN (atac 1));
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by ((dres_inst_tac [("a","$ s a")] new_tv_W 1) THEN (atac 1));
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by (safe_tac HOL_cs);
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  by (best_tac (HOL_cs addDs[sym RS W_var_geD,new_tv_subst_le,new_tv_list_le] 
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                       addss !simpset) 1);
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 by (fast_tac (HOL_cs addDs [sym RS W_var_geD,new_tv_subst_le,new_tv_list_le] 
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                      addss !simpset) 1);
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(** LEVEL 79 **)
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by (dres_inst_tac [("e","expr1")] (sym RS W_var_geD) 1);
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by ((dtac new_tv_subst_tel 1) THEN (atac 1));
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by ((dres_inst_tac [("ts","$ s a")] new_tv_list_le 1) THEN (atac 1));
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by ((dtac new_tv_subst_tel 1) THEN (atac 1));
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by (best_tac (HOL_cs addDs [new_tv_W] 
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                     addss (!simpset addsimps [subst_comp_tel])) 1);
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(** LEVEL 84 **)
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qed_spec_mp "I_correct_wrt_W";
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(***
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We actually want the corollary
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goal I.thy
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  "I e [] m id_subst = Ok(s,t,n) --> W e [] m = Ok(s, $s t, n)";
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by (cut_facts_tac [(read_instantiate[("x","id_subst")]
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 (read_instantiate[("x","[]")](thm RS spec)
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  RS spec RS spec))] 1);
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by (Full_simp_tac 1);
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by (fast_tac HOL_cs 1);
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qed;
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assuming that thm is the undischarged version of I_correct_wrt_W.
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Wait until simplification of thms is possible.
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***)
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val lemma = I_correct_wrt_W COMP swap_prems_rl;
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goal I.thy "!a m s. \
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\  new_tv m a & new_tv m s --> I e a m s = Fail --> W e ($s a) m = Fail";
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by (expr.induct_tac "e" 1);
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  by (simp_tac (!simpset addsimps [app_subst_list]
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                        setloop (split_tac [expand_if])) 1);
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 by (Simp_tac 1);
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   142
 by (strip_tac 1);
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   143
 by (rtac conjI 1);
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   144
  by (strip_tac 1);
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   145
  by (subgoal_tac "TVar m # $ s a = $s(TVar m # a)" 1);
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   146
   by (asm_simp_tac (HOL_ss addsimps
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        [new_tv_Suc_list, lessI RS less_imp_le RS new_tv_subst_le]) 1);
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   148
  by (etac conjE 1);
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   149
  by (dtac (new_tv_not_free_tv RS not_free_impl_id) 1);
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   150
  by (Asm_simp_tac 1);
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   151
 by (strip_tac 1);
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   152
 by (etac exE 1);
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   153
 by (split_all_tac 1);
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   154
 by (Full_simp_tac 1);
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   155
(** LEVEL 15 **)
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by (Asm_simp_tac 1);
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   157
by (strip_tac 1);
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   158
by (etac exE 1);
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   159
by (REPEAT(etac conjE 1));
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   160
by (split_all_tac 1);
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   161
by (Full_simp_tac 1);
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   162
by (dtac lemma 1);
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   163
 by (fast_tac HOL_cs 1);
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   164
(** LEVEL 23 **)
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by (etac exE 1);
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   166
by (etac conjE 1);
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   167
by (hyp_subst_tac 1);
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   168
by (Asm_simp_tac 1);
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   169
by (etac disjE 1);
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 by (rtac disjI1 1);
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   171
(** LEVEL 29 **)
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 by (full_simp_tac (!simpset addsimps [o_def,subst_comp_tel]) 1);
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   173
 by (EVERY[etac allE 1, etac allE 1, etac allE 1,
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          etac impE 1, etac impE 2, atac 2, atac 2]);
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 by (rtac conjI 1);
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   176
  by (fast_tac (HOL_cs addIs [W_var_ge RS new_tv_list_le]) 1);
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 by (rtac new_tv_subst_comp_2 1);
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   178
  by (fast_tac (HOL_cs addIs [W_var_ge RS new_tv_subst_le]) 1);
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   179
 by (fast_tac (HOL_cs addSIs [new_tv_subst_tel]addIs[new_tv_W RS conjunct1])1);
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   180
by (rtac disjI2 1);
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   181
by (etac exE 1);
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   182
by (split_all_tac 1);
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   183
by (etac conjE 1);
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   184
(** LEVEL 40 **)
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   185
by (Full_simp_tac 1);
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   186
by (dtac lemma 1);
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   187
 by (rtac conjI 1);
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diff changeset
   188
  by (fast_tac (HOL_cs addIs [W_var_ge RS new_tv_list_le]) 1);
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   189
 by (rtac new_tv_subst_comp_1 1);
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diff changeset
   190
   by (fast_tac (HOL_cs addIs [W_var_ge RS new_tv_subst_le]) 1);
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diff changeset
   191
 by (fast_tac (HOL_cs addSIs [new_tv_subst_tel]addIs[new_tv_W RS conjunct1])1);
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   192
by (etac exE 1);
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diff changeset
   193
by (etac conjE 1);
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   194
by (hyp_subst_tac 1);
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diff changeset
   195
(** LEVEL 50 **)
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   196
by (asm_full_simp_tac (!simpset addsimps
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   197
     [o_def,subst_comp_te RS sym,subst_comp_tel RS sym]) 1);
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   198
qed_spec_mp "I_complete_wrt_W";
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diff changeset
   199
946efd210837 Added thm I_complete_wrt_W to I.
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   200
(***
946efd210837 Added thm I_complete_wrt_W to I.
nipkow
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   201
We actually want the corollary
946efd210837 Added thm I_complete_wrt_W to I.
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diff changeset
   202
946efd210837 Added thm I_complete_wrt_W to I.
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   203
  "I e [] m id_subst = Fail ==> W e [] m = Fail";
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   204
946efd210837 Added thm I_complete_wrt_W to I.
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   205
Wait until simplification of thms is possible.
946efd210837 Added thm I_complete_wrt_W to I.
nipkow
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diff changeset
   206
***)