src/HOL/MiniML/I.ML
author nipkow
Mon, 22 Apr 1996 15:42:20 +0200
changeset 1669 e56cdf711729
parent 1486 7b95d7b49f7a
child 1673 d22110ddd0af
permissions -rw-r--r--
inserted Suc_less_eq explictly in a few proofs. inserted o_def explictly in a few proofs because the new split_tac causes fewer eta-expansions which some of the rewrites need. Indented proof in I.ML
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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_tac [expand_if])) 1);
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  by (fast_tac (HOL_cs addss !simpset) 1);
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 (* case Abs e *)
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 by (asm_full_simp_tac (!simpset setloop (split_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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 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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(* case App e1 e2 *)
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by (simp_tac (!simpset setloop (split_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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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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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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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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by (rtac exI 1);
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by (safe_tac HOL_cs);
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  by (fast_tac HOL_cs 1);
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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 (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 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 (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 (fast_tac (HOL_cs addDs [new_tv_W] addss 
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    (!simpset addsimps [subst_comp_tel])) 1);
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qed_spec_mp "I_correct_wrt_W";