# HG changeset patch
# User blanchet
# Date 1347909210 -7200
# Node ID 6d05b8452cf31ae001f3f1b1c1bce0bf36382f5c
# Parent  f27f83f71e94e6298ff612ce15b2241486cd3000
got rid of one "auto" in induction tactic

diff -r f27f83f71e94 -r 6d05b8452cf3 src/HOL/Codatatype/BNF_FP.thy
--- a/src/HOL/Codatatype/BNF_FP.thy	Mon Sep 17 16:57:22 2012 +0200
+++ b/src/HOL/Codatatype/BNF_FP.thy	Mon Sep 17 21:13:30 2012 +0200
@@ -104,11 +104,25 @@
 "sum_case f g (if p then Inl x else Inr y) = (if p then f x else g y)"
 by simp
 
-lemma UN_compreh_bex:
-"\<Union>{y. \<exists>x \<in> A. y = {}} = {}"
-"\<Union>{y. \<exists>x \<in> A. y = {f x}} = {y. \<exists>x \<in> A. y = f x}"
+lemma UN_compreh_bex_eq_empty:
+"\<Union>{y. \<exists>x\<in>A. y = {}} = {}"
+by blast
+
+lemma UN_compreh_bex_eq_singleton:
+"\<Union>{y. \<exists>x\<in>A. y = {f x}} = {y. \<exists>x\<in>A. y = f x}"
+by blast
+
+lemma mem_UN_comprehI:
+"z \<in> {y. \<exists>x\<in>A. y = f x} \<Longrightarrow> z \<in> \<Union>{y. \<exists>x\<in>A. y = {f x}}"
+"z \<in> {y. \<exists>x\<in>A. y = f x} \<union> B \<Longrightarrow> z \<in> \<Union>{y. \<exists>x\<in>A. y = {f x}} \<union> B"
+"z \<in> \<Union>{y. \<exists>x\<in>A. y = F x} \<union> \<Union>{y. \<exists>x\<in>A. y = G x} \<Longrightarrow> z \<in> \<Union>{y. \<exists>x\<in>A. y = F x \<union> G x}"
+"z \<in> \<Union>{y. \<exists>x\<in>A. y = F x} \<union> (\<Union>{y. \<exists>x\<in>A. y = G x} \<union> B) \<Longrightarrow> z \<in> \<Union>{y. \<exists>x\<in>A. y = F x \<union> G x} \<union> B"
 by blast+
 
+lemma mem_UN_comprehI':
+"\<exists>y. (\<exists>x\<in>A. y = F x) \<and> z \<in> y \<Longrightarrow> z \<in> \<Union>{y. \<exists>x\<in>A. y = {y. \<exists>y'\<in>F x. y = y'}}"
+by blast
+
 lemma induct_set_step: "\<lbrakk>B \<in> A; c \<in> f B\<rbrakk> \<Longrightarrow> \<exists>C. (\<exists>a \<in> A. C = f a) \<and> c \<in> C"
 apply (rule exI)
 apply (rule conjI)
diff -r f27f83f71e94 -r 6d05b8452cf3 src/HOL/Codatatype/Tools/bnf_fp_sugar.ML
--- a/src/HOL/Codatatype/Tools/bnf_fp_sugar.ML	Mon Sep 17 16:57:22 2012 +0200
+++ b/src/HOL/Codatatype/Tools/bnf_fp_sugar.ML	Mon Sep 17 21:13:30 2012 +0200
@@ -499,7 +499,9 @@
     val nesting_map_ids = map map_id_of_bnf nesting_bnfs;
 
     fun mk_map live Ts Us t =
-      let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last in
+      let
+        val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last
+      in
         Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
       end;
 
diff -r f27f83f71e94 -r 6d05b8452cf3 src/HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML
--- a/src/HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML	Mon Sep 17 16:57:22 2012 +0200
+++ b/src/HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML	Mon Sep 17 21:13:30 2012 +0200
@@ -97,10 +97,17 @@
        etac @{thm induct_set_step}) THEN'
     atac ORELSE' SELECT_GOAL (auto_tac ctxt);
 
+fun gen_UN_comprehI_tac UnI = REPEAT_DETERM o resolve_tac @{thms mem_UN_comprehI} THEN' rtac UnI;
+
+fun gen_UnIN_tac 1 1 = REPEAT_DETERM o resolve_tac @{thms mem_UN_comprehI'}
+  | gen_UnIN_tac _ 1 = gen_UN_comprehI_tac @{thm UnI1} THEN' gen_UnIN_tac 1 1
+  | gen_UnIN_tac n k = gen_UN_comprehI_tac @{thm UnI2} THEN' gen_UnIN_tac (n - 1) (k - 1);
+
 val induct_prem_prem_thms =
-  @{thms SUP_empty Sup_empty Sup_insert UN_compreh_bex UN_insert Un_assoc[symmetric] Un_empty_left
-      Un_empty_right Union_Un_distrib collect_def[abs_def] fst_conv image_def o_apply snd_conv
-      snd_prod_fun sum.cases sup_bot_right fst_map_pair map_pair_simp sum_map.simps};
+  @{thms SUP_empty Sup_empty Sup_insert UN_compreh_bex_eq_empty UN_compreh_bex_eq_singleton
+      UN_insert Un_assoc Un_empty_left Un_empty_right Union_Un_distrib collect_def[abs_def] fst_conv
+      image_def o_apply snd_conv snd_prod_fun sum.cases sup_bot_right fst_map_pair map_pair_simp
+      sum_map.simps};
 
 (* These rules interfere with the "set_natural'" properties of "sum" and "prod", so we explicitly
    delay them. *)
@@ -114,8 +121,7 @@
        (pre_set_defs @ set_natural's @ induct_prem_prem_thms)),
      SELECT_GOAL (Local_Defs.unfold_tac ctxt
        (induct_prem_prem_thms_delayed @ induct_prem_prem_thms)),
-     rtac (mk_UnIN pp jj) THEN' mk_induct_prem_prem_endgame_tac ctxt qq ORELSE'
-       SELECT_GOAL (auto_tac ctxt)]) (rev ppjjqqkks)) 1;
+     gen_UnIN_tac pp jj THEN' mk_induct_prem_prem_endgame_tac ctxt qq]) (rev ppjjqqkks)) 1;
 
 fun mk_induct_discharge_prem_tac ctxt nn n set_natural's pre_set_defs m k ppjjqqkks =
   let val r = length ppjjqqkks in