renamed BNF fact
authorblanchet
Thu, 29 Aug 2013 23:01:04 +0200
changeset 53290 b6c3be868217
parent 53289 5e0623448bdb
child 53299 84242070e267
renamed BNF fact
src/HOL/BNF/Examples/Stream.thy
src/HOL/BNF/Examples/TreeFI.thy
src/HOL/BNF/More_BNFs.thy
src/HOL/BNF/Tools/bnf_def.ML
src/HOL/BNF/Tools/bnf_def_tactics.ML
src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
src/HOL/BNF/Tools/bnf_fp_def_sugar_tactics.ML
src/HOL/BNF/Tools/bnf_gfp.ML
src/HOL/BNF/Tools/bnf_lfp.ML
src/HOL/BNF/Tools/bnf_lfp_tactics.ML
--- a/src/HOL/BNF/Examples/Stream.thy	Thu Aug 29 22:56:39 2013 +0200
+++ b/src/HOL/BNF/Examples/Stream.thy	Thu Aug 29 23:01:04 2013 +0200
@@ -453,12 +453,12 @@
 proof (cases "n \<le> m")
   case False thus ?thesis unfolding smerge_def
     by (subst sset_flat)
-      (auto simp: stream.set_map' in_set_conv_nth simp del: stake.simps
+      (auto simp: stream.set_map in_set_conv_nth simp del: stake.simps
         intro!: exI[of _ n, OF disjI2] exI[of _ m, OF mp])
 next
   case True thus ?thesis unfolding smerge_def
     by (subst sset_flat)
-      (auto simp: stream.set_map' in_set_conv_nth image_iff simp del: stake.simps snth.simps
+      (auto simp: stream.set_map in_set_conv_nth image_iff simp del: stake.simps snth.simps
         intro!: exI[of _ m, OF disjI1] bexI[of _ "ss !! n"] exI[of _ n, OF mp])
 qed
 
@@ -467,7 +467,7 @@
   fix x assume "x \<in> sset (smerge ss)"
   thus "x \<in> UNION (sset ss) sset"
     unfolding smerge_def by (subst (asm) sset_flat)
-      (auto simp: stream.set_map' in_set_conv_nth sset_range simp del: stake.simps, fast+)
+      (auto simp: stream.set_map in_set_conv_nth sset_range simp del: stake.simps, fast+)
 next
   fix s x assume "s \<in> sset ss" "x \<in> sset s"
   thus "x \<in> sset (smerge ss)" using snth_sset_smerge by (auto simp: sset_range)
@@ -480,7 +480,7 @@
   "sproduct s1 s2 = smerge (smap (\<lambda>x. smap (Pair x) s2) s1)"
 
 lemma sset_sproduct: "sset (sproduct s1 s2) = sset s1 \<times> sset s2"
-  unfolding sproduct_def sset_smerge by (auto simp: stream.set_map')
+  unfolding sproduct_def sset_smerge by (auto simp: stream.set_map)
 
 
 subsection {* interleave two streams *}
--- a/src/HOL/BNF/Examples/TreeFI.thy	Thu Aug 29 22:56:39 2013 +0200
+++ b/src/HOL/BNF/Examples/TreeFI.thy	Thu Aug 29 23:01:04 2013 +0200
@@ -16,7 +16,7 @@
 
 lemma pre_treeFI_listF_set[simp]: "pre_treeFI_set2 (i, xs) = listF_set xs"
 unfolding pre_treeFI_set2_def collect_def[abs_def] prod_set_defs
-by (auto simp add: listF.set_map')
+by (auto simp add: listF.set_map)
 
 lemma dtor[simp]: "treeFI_dtor tr = (lab tr, sub tr)"
 by (metis Tree_def treeFI.collapse treeFI.dtor_ctor)
--- a/src/HOL/BNF/More_BNFs.thy	Thu Aug 29 22:56:39 2013 +0200
+++ b/src/HOL/BNF/More_BNFs.thy	Thu Aug 29 23:01:04 2013 +0200
@@ -227,7 +227,7 @@
 apply transfer apply simp
 done
 
-lemmas [simp] = fset.map_comp fset.map_id fset.set_map'
+lemmas [simp] = fset.map_comp fset.map_id fset.set_map
 
 lemma fset_rel_fset: "set_rel \<chi> (fset A1) (fset A2) = fset_rel \<chi> A1 A2"
   unfolding fset_rel_def set_rel_def by auto
@@ -881,7 +881,7 @@
 Plus: "\<lbrakk>R a b; multiset_rel' R M N\<rbrakk> \<Longrightarrow> multiset_rel' R (M + {#a#}) (N + {#b#})"
 
 lemma multiset_map_Zero_iff[simp]: "mmap f M = {#} \<longleftrightarrow> M = {#}"
-by (metis image_is_empty multiset.set_map' set_of_eq_empty_iff)
+by (metis image_is_empty multiset.set_map set_of_eq_empty_iff)
 
 lemma multiset_map_Zero[simp]: "mmap f {#} = {#}" by simp
 
@@ -1001,7 +1001,7 @@
 shows "\<exists> N1. N = N1 + {#f a#} \<and> mmap f M = N1"
 proof-
   have "f a \<in># N"
-  using assms multiset.set_map'[of f "M + {#a#}"] by auto
+  using assms multiset.set_map[of f "M + {#a#}"] by auto
   then obtain N1 where N: "N = N1 + {#f a#}" using multi_member_split by metis
   have "mmap f M = N1" using assms unfolding N by simp
   thus ?thesis using N by blast
@@ -1012,7 +1012,7 @@
 shows "\<exists> M1 a. M = M1 + {#a#} \<and> f a = b \<and> mmap f M1 = N"
 proof-
   obtain a where a: "a \<in># M" and fa: "f a = b"
-  using multiset.set_map'[of f M] unfolding assms
+  using multiset.set_map[of f M] unfolding assms
   by (metis image_iff mem_set_of_iff union_single_eq_member)
   then obtain M1 where M: "M = M1 + {#a#}" using multi_member_split by metis
   have "mmap f M1 = N" using assms unfolding M fa[symmetric] by simp
--- a/src/HOL/BNF/Tools/bnf_def.ML	Thu Aug 29 22:56:39 2013 +0200
+++ b/src/HOL/BNF/Tools/bnf_def.ML	Thu Aug 29 23:01:04 2013 +0200
@@ -73,7 +73,7 @@
   val set_bd_of_bnf: bnf -> thm list
   val set_defs_of_bnf: bnf -> thm list
   val set_map0_of_bnf: bnf -> thm list
-  val set_map'_of_bnf: bnf -> thm list
+  val set_map_of_bnf: bnf -> thm list
   val wit_thms_of_bnf: bnf -> thm list
   val wit_thmss_of_bnf: bnf -> thm list list
 
@@ -195,7 +195,7 @@
   map_wppull: thm lazy,
   rel_eq: thm lazy,
   rel_flip: thm lazy,
-  set_map': thm lazy list,
+  set_map: thm lazy list,
   rel_cong: thm lazy,
   rel_mono: thm lazy,
   rel_mono_strong: thm lazy,
@@ -205,7 +205,7 @@
 };
 
 fun mk_facts bd_Card_order bd_Cinfinite bd_Cnotzero collect_set_map in_bd in_cong in_mono in_rel
-    map_comp map_cong map_id map_transfer map_wppull rel_eq rel_flip set_map' rel_cong rel_mono
+    map_comp map_cong map_id map_transfer map_wppull rel_eq rel_flip set_map rel_cong rel_mono
     rel_mono_strong rel_Grp rel_conversep rel_OO = {
   bd_Card_order = bd_Card_order,
   bd_Cinfinite = bd_Cinfinite,
@@ -222,7 +222,7 @@
   map_wppull = map_wppull,
   rel_eq = rel_eq,
   rel_flip = rel_flip,
-  set_map' = set_map',
+  set_map = set_map,
   rel_cong = rel_cong,
   rel_mono = rel_mono,
   rel_mono_strong = rel_mono_strong,
@@ -246,7 +246,7 @@
   map_wppull,
   rel_eq,
   rel_flip,
-  set_map',
+  set_map,
   rel_cong,
   rel_mono,
   rel_mono_strong,
@@ -268,7 +268,7 @@
     map_wppull = Lazy.map f map_wppull,
     rel_eq = Lazy.map f rel_eq,
     rel_flip = Lazy.map f rel_flip,
-    set_map' = map (Lazy.map f) set_map',
+    set_map = map (Lazy.map f) set_map,
     rel_cong = Lazy.map f rel_cong,
     rel_mono = Lazy.map f rel_mono,
     rel_mono_strong = Lazy.map f rel_mono_strong,
@@ -395,7 +395,7 @@
 val set_bd_of_bnf = #set_bd o #axioms o rep_bnf;
 val set_defs_of_bnf = #set_defs o #defs o rep_bnf;
 val set_map0_of_bnf = #set_map0 o #axioms o rep_bnf;
-val set_map'_of_bnf = map Lazy.force o #set_map' o #facts o rep_bnf;
+val set_map_of_bnf = map Lazy.force o #set_map o #facts o rep_bnf;
 val rel_cong_of_bnf = Lazy.force o #rel_cong o #facts o rep_bnf;
 val rel_mono_of_bnf = Lazy.force o #rel_mono o #facts o rep_bnf;
 val rel_mono_strong_of_bnf = Lazy.force o #rel_mono_strong o #facts o rep_bnf;
@@ -519,7 +519,7 @@
 val rel_eqN = "rel_eq";
 val rel_flipN = "rel_flip";
 val set_map0N = "set_map0";
-val set_map'N = "set_map'";
+val set_mapN = "set_map";
 val set_bdN = "set_bd";
 val rel_GrpN = "rel_Grp";
 val rel_conversepN = "rel_conversep";
@@ -583,7 +583,7 @@
             (map_idN, [Lazy.force (#map_id facts)], []),
             (rel_eqN, [Lazy.force (#rel_eq facts)], []),
             (rel_flipN, [Lazy.force (#rel_flip facts)], []),
-            (set_map'N, map Lazy.force (#set_map' facts), []),
+            (set_mapN, map Lazy.force (#set_map facts), []),
             (rel_OO_GrpN, no_refl [#rel_OO_Grp axioms], []),
             (rel_GrpN, [Lazy.force (#rel_Grp facts)], []),
             (rel_conversepN, [Lazy.force (#rel_conversep facts)], []),
@@ -1018,7 +1018,7 @@
 
         val map_cong = Lazy.lazy mk_map_cong;
 
-        val set_map' = map (fn thm => Lazy.lazy (fn () => mk_set_map' thm)) (#set_map0 axioms);
+        val set_map = map (fn thm => Lazy.lazy (fn () => mk_set_map thm)) (#set_map0 axioms);
 
         fun mk_in_bd () =
           let
@@ -1050,7 +1050,7 @@
             Goal.prove_sorry lthy [] [] in_bd_goal
               (mk_in_bd_tac live surj_imp_ordLeq_inst
                 (Lazy.force map_comp) (Lazy.force map_id) (#map_cong0 axioms)
-                (map Lazy.force set_map') (#set_bd axioms) (#bd_card_order axioms)
+                (map Lazy.force set_map) (#set_bd axioms) (#bd_card_order axioms)
                 bd_Card_order bd_Cinfinite bd_Cnotzero)
             |> Thm.close_derivation
           end;
@@ -1087,7 +1087,7 @@
           in
             Goal.prove_sorry lthy [] [] goal
               (fn _ => mk_map_wppull_tac (#map_id0 axioms) (#map_cong0 axioms)
-                (#map_wpull axioms) (Lazy.force map_comp) (map Lazy.force set_map'))
+                (#map_wpull axioms) (Lazy.force map_comp) (map Lazy.force set_map))
             |> Thm.close_derivation
           end;
 
@@ -1103,7 +1103,7 @@
           in
             Goal.prove_sorry lthy [] [] goal
               (mk_rel_Grp_tac rel_OO_Grps (#map_id0 axioms) (#map_cong0 axioms) (Lazy.force map_id)
-                (Lazy.force map_comp) (map Lazy.force set_map'))
+                (Lazy.force map_comp) (map Lazy.force set_map))
             |> Thm.close_derivation
           end;
 
@@ -1155,7 +1155,7 @@
             val le_goal = fold_rev Logic.all Rs (HOLogic.mk_Trueprop (mk_leq lhs rhs));
             val le_thm = Goal.prove_sorry lthy [] [] le_goal
               (mk_rel_conversep_le_tac rel_OO_Grps (Lazy.force rel_eq) (#map_cong0 axioms)
-                (Lazy.force map_comp) (map Lazy.force set_map'))
+                (Lazy.force map_comp) (map Lazy.force set_map))
               |> Thm.close_derivation
             val goal = fold_rev Logic.all Rs (mk_Trueprop_eq (lhs, rhs));
           in
@@ -1176,7 +1176,7 @@
           in
             Goal.prove_sorry lthy [] [] goal
               (mk_rel_OO_tac rel_OO_Grps (Lazy.force rel_eq) (#map_cong0 axioms)
-                (Lazy.force map_wppull) (Lazy.force map_comp) (map Lazy.force set_map'))
+                (Lazy.force map_wppull) (Lazy.force map_comp) (map Lazy.force set_map))
             |> Thm.close_derivation
           end;
 
@@ -1227,7 +1227,7 @@
           in
             Goal.prove_sorry lthy [] []
               (fold_rev Logic.all (x :: y :: Rs @ Rs_copy) (Logic.list_implies (prems, concl)))
-              (mk_rel_mono_strong_tac (Lazy.force in_rel) (map Lazy.force set_map'))
+              (mk_rel_mono_strong_tac (Lazy.force in_rel) (map Lazy.force set_map))
             |> Thm.close_derivation
           end;
 
@@ -1245,7 +1245,7 @@
             Goal.prove_sorry lthy [] []
               (fold_rev Logic.all (transfer_domRs @ transfer_ranRs) concl)
               (mk_map_transfer_tac (Lazy.force rel_mono) (Lazy.force in_rel)
-                (map Lazy.force set_map') (#map_cong0 axioms) (Lazy.force map_comp))
+                (map Lazy.force set_map) (#map_cong0 axioms) (Lazy.force map_comp))
             |> Thm.close_derivation
           end;
 
@@ -1254,7 +1254,7 @@
         val defs = mk_defs bnf_map_def bnf_set_defs bnf_rel_def;
 
         val facts = mk_facts bd_Card_order bd_Cinfinite bd_Cnotzero collect_set_map in_bd in_cong
-          in_mono in_rel map_comp map_cong map_id map_transfer map_wppull rel_eq rel_flip set_map'
+          in_mono in_rel map_comp map_cong map_id map_transfer map_wppull rel_eq rel_flip set_map
           rel_cong rel_mono rel_mono_strong rel_Grp rel_conversep rel_OO;
 
         val wits = map2 mk_witness bnf_wits wit_thms;
--- a/src/HOL/BNF/Tools/bnf_def_tactics.ML	Thu Aug 29 22:56:39 2013 +0200
+++ b/src/HOL/BNF/Tools/bnf_def_tactics.ML	Thu Aug 29 23:01:04 2013 +0200
@@ -14,7 +14,7 @@
   val mk_map_cong_tac: Proof.context -> thm -> tactic
   val mk_in_mono_tac: int -> tactic
   val mk_map_wppull_tac: thm -> thm -> thm -> thm -> thm list -> tactic
-  val mk_set_map': thm -> thm
+  val mk_set_map: thm -> thm
 
   val mk_rel_Grp_tac: thm list -> thm -> thm -> thm -> thm -> thm list ->
     {prems: thm list, context: Proof.context} -> tactic
@@ -50,7 +50,7 @@
 fun mk_map_cong_tac ctxt cong0 =
   (hyp_subst_tac ctxt THEN' rtac cong0 THEN'
    REPEAT_DETERM o (dtac meta_spec THEN' etac meta_mp THEN' atac)) 1;
-fun mk_set_map' set_map0 = set_map0 RS @{thm comp_eq_dest};
+fun mk_set_map set_map0 = set_map0 RS @{thm comp_eq_dest};
 fun mk_in_mono_tac n = if n = 0 then rtac subset_UNIV 1
   else (rtac subsetI THEN'
   rtac CollectI) 1 THEN
@@ -226,10 +226,10 @@
     EVERY' [rtac exI, rtac @{thm conjI[OF CollectI conjI[OF refl refl]]},
       CONJ_WRAP' (K (etac @{thm Collect_split_mono_strong} THEN' atac)) set_map0s] 1;
 
-fun mk_map_transfer_tac rel_mono in_rel set_map's map_cong0 map_comp
+fun mk_map_transfer_tac rel_mono in_rel set_maps map_cong0 map_comp
   {context = ctxt, prems = _} =
   let
-    val n = length set_map's;
+    val n = length set_maps;
   in
     REPEAT_DETERM_N n (HEADGOAL (rtac @{thm fun_relI})) THEN
     unfold_thms_tac ctxt @{thms fun_rel_iff_leq_vimage2p} THEN
@@ -239,14 +239,14 @@
       rtac @{thm vimage2pI}, rtac (in_rel RS iffD2), rtac exI, rtac conjI, rtac CollectI,
       CONJ_WRAP' (fn thm =>
         etac (thm RS @{thm ord_eq_le_trans[OF _ subset_trans[OF image_mono convol_image_vimage2p]]}))
-      set_map's,
+      set_maps,
       rtac conjI,
       EVERY' (map (fn convol =>
         rtac (box_equals OF [map_cong0, map_comp RS sym, map_comp RS sym]) THEN'
         REPEAT_DETERM_N n o rtac (convol RS fun_cong)) @{thms fst_convol snd_convol})])
   end;
 
-fun mk_in_bd_tac live surj_imp_ordLeq_inst map_comp map_id map_cong0 set_map's set_bds
+fun mk_in_bd_tac live surj_imp_ordLeq_inst map_comp map_id map_cong0 set_maps set_bds
   bd_card_order bd_Card_order bd_Cinfinite bd_Cnotzero {context = ctxt, prems = _} =
   if live = 0 then
     rtac @{thm ordLeq_transitive[OF ordLeq_csum2[OF card_of_Card_order]
@@ -272,7 +272,7 @@
         rtac bd_Card_order, rtac @{thm Card_order_csum}, rtac bd_Cnotzero,
         rtac @{thm csum_Cfinite_cexp_Cinfinite},
         rtac (if live = 1 then @{thm card_of_Card_order} else @{thm Card_order_csum}),
-        CONJ_WRAP_GEN' (rtac @{thm Cfinite_csum}) (K (rtac @{thm Cfinite_cone})) set_map's,
+        CONJ_WRAP_GEN' (rtac @{thm Cfinite_csum}) (K (rtac @{thm Cfinite_cone})) set_maps,
         rtac bd'_Cinfinite, rtac @{thm card_of_Card_order},
         rtac @{thm Card_order_cexp}, rtac @{thm Cinfinite_cexp}, rtac @{thm ordLeq_csum2},
         rtac @{thm Card_order_ctwo}, rtac bd'_Cinfinite,
@@ -290,7 +290,7 @@
         else REPEAT_DETERM_N (live - 2) o (etac conjE THEN' rotate_tac ~1) THEN' etac conjE,
         rtac (Drule.rotate_prems 1 @{thm image_eqI}), rtac @{thm SigmaI}, rtac @{thm UNIV_I},
         CONJ_WRAP_GEN' (rtac @{thm SigmaI})
-          (K (etac @{thm If_the_inv_into_in_Func} THEN' atac)) set_map's,
+          (K (etac @{thm If_the_inv_into_in_Func} THEN' atac)) set_maps,
         rtac sym,
         rtac (Drule.rotate_prems 1
            ((box_equals OF [map_cong0 OF replicate live @{thm If_the_inv_into_f_f},
@@ -302,7 +302,7 @@
         REPEAT_DETERM o eresolve_tac [CollectE, conjE], rtac CollectI,
         CONJ_WRAP' (fn thm =>
           rtac (thm RS ord_eq_le_trans) THEN' etac @{thm subset_trans[OF image_mono Un_upper1]})
-        set_map's,
+        set_maps,
         rtac sym,
         rtac (box_equals OF [map_cong0 OF replicate live @{thm fun_cong[OF sum_case_o_inj(1)]},
            map_comp RS sym, map_id])] 1
--- a/src/HOL/BNF/Tools/bnf_fp_def_sugar.ML	Thu Aug 29 22:56:39 2013 +0200
+++ b/src/HOL/BNF/Tools/bnf_fp_def_sugar.ML	Thu Aug 29 23:01:04 2013 +0200
@@ -604,7 +604,7 @@
     val pre_set_defss = map set_defs_of_bnf pre_bnfs;
     val nesting_map_id's = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nesting_bnfs;
     val nested_map_id's = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nested_bnfs;
-    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
+    val nested_set_maps = maps set_map_of_bnf nested_bnfs;
 
     val fp_b_names = map base_name_of_typ fpTs;
 
@@ -687,7 +687,7 @@
 
         val thm =
           Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
-            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
+            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_maps
               pre_set_defss)
           |> singleton (Proof_Context.export names_lthy lthy)
           |> Thm.close_derivation;
@@ -1170,8 +1170,8 @@
     val pre_map_defs = map map_def_of_bnf pre_bnfs;
     val pre_set_defss = map set_defs_of_bnf pre_bnfs;
     val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
-    val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
-    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
+    val nesting_set_maps = maps set_map_of_bnf nesting_bnfs;
+    val nested_set_maps = maps set_map_of_bnf nested_bnfs;
 
     val live = live_of_bnf any_fp_bnf;
     val _ =
@@ -1330,7 +1330,7 @@
 
               fun mk_set_thm fp_set_thm ctr_def' cxIn =
                 fold_thms lthy [ctr_def']
-                  (unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
+                  (unfold_thms lthy (pre_set_defs @ nested_set_maps @ nesting_set_maps @
                        (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_set)
                      (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
                 |> singleton (Proof_Context.export names_lthy no_defs_lthy);
--- a/src/HOL/BNF/Tools/bnf_fp_def_sugar_tactics.ML	Thu Aug 29 22:56:39 2013 +0200
+++ b/src/HOL/BNF/Tools/bnf_fp_def_sugar_tactics.ML	Thu Aug 29 23:01:04 2013 +0200
@@ -119,26 +119,26 @@
     hyp_subst_tac ctxt ORELSE' resolve_tac @{thms disjI1 disjI2}) THEN'
   (rtac refl ORELSE' atac ORELSE' rtac @{thm singletonI});
 
-fun mk_induct_leverage_prem_prems_tac ctxt nn kks set_map's pre_set_defs =
+fun mk_induct_leverage_prem_prems_tac ctxt nn kks set_maps pre_set_defs =
   HEADGOAL (EVERY' (maps (fn kk => [select_prem_tac nn (dtac meta_spec) kk, etac meta_mp,
-    SELECT_GOAL (unfold_thms_tac ctxt (pre_set_defs @ set_map's @ sum_prod_thms_set0)),
+    SELECT_GOAL (unfold_thms_tac ctxt (pre_set_defs @ set_maps @ sum_prod_thms_set0)),
     solve_prem_prem_tac ctxt]) (rev kks)));
 
-fun mk_induct_discharge_prem_tac ctxt nn n set_map's pre_set_defs m k kks =
+fun mk_induct_discharge_prem_tac ctxt nn n set_maps pre_set_defs m k kks =
   let val r = length kks in
     HEADGOAL (EVERY' [select_prem_tac n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac ctxt,
       REPEAT_DETERM_N m o (dtac meta_spec THEN' rotate_tac ~1)]) THEN
     EVERY [REPEAT_DETERM_N r
         (HEADGOAL (rotate_tac ~1 THEN' dtac meta_mp THEN' rotate_tac 1) THEN prefer_tac 2),
       if r > 0 then ALLGOALS Goal.norm_hhf_tac else all_tac, HEADGOAL atac,
-      mk_induct_leverage_prem_prems_tac ctxt nn kks set_map's pre_set_defs]
+      mk_induct_leverage_prem_prems_tac ctxt nn kks set_maps pre_set_defs]
   end;
 
-fun mk_induct_tac ctxt nn ns mss kkss ctr_defs ctor_induct' set_map's pre_set_defss =
+fun mk_induct_tac ctxt nn ns mss kkss ctr_defs ctor_induct' set_maps pre_set_defss =
   let val n = Integer.sum ns in
     unfold_thms_tac ctxt ctr_defs THEN
     HEADGOAL (rtac ctor_induct' THEN' inst_as_projs_tac ctxt) THEN
-    EVERY (map4 (EVERY oooo map3 o mk_induct_discharge_prem_tac ctxt nn n set_map's) pre_set_defss
+    EVERY (map4 (EVERY oooo map3 o mk_induct_discharge_prem_tac ctxt nn n set_maps) pre_set_defss
       mss (unflat mss (1 upto n)) kkss)
   end;
 
--- a/src/HOL/BNF/Tools/bnf_gfp.ML	Thu Aug 29 22:56:39 2013 +0200
+++ b/src/HOL/BNF/Tools/bnf_gfp.ML	Thu Aug 29 23:01:04 2013 +0200
@@ -222,7 +222,7 @@
     val map_ids = map map_id_of_bnf bnfs;
     val map_wpulls = map map_wpull_of_bnf bnfs;
     val set_bdss = map set_bd_of_bnf bnfs;
-    val set_map'ss = map set_map'_of_bnf bnfs;
+    val set_mapss = map set_map_of_bnf bnfs;
     val rel_congs = map rel_cong_of_bnf bnfs;
     val rel_converseps = map rel_conversep_of_bnf bnfs;
     val rel_Grps = map rel_Grp_of_bnf bnfs;
@@ -809,7 +809,7 @@
         Goal.prove_sorry lthy [] []
           (fold_rev Logic.all (As @ Bs @ ss @ B's @ s's @ Rs)
             (mk_Trueprop_eq (mk_bis As Bs ss B's s's Rs, rhs)))
-          (K (mk_bis_rel_tac lthy m bis_def rel_OO_Grps map_comps map_cong0s set_map'ss))
+          (K (mk_bis_rel_tac lthy m bis_def rel_OO_Grps map_comps map_cong0s set_mapss))
         |> Thm.close_derivation
       end;
 
@@ -1209,7 +1209,7 @@
     val coalgT_thm =
       Goal.prove_sorry lthy [] []
         (fold_rev Logic.all As (HOLogic.mk_Trueprop (mk_coalg As carTAs strTAs)))
-        (mk_coalgT_tac m (coalg_def :: isNode_defs @ carT_defs) strT_defs set_map'ss)
+        (mk_coalgT_tac m (coalg_def :: isNode_defs @ carT_defs) strT_defs set_mapss)
       |> Thm.close_derivation;
 
     val timer = time (timer "Tree coalgebra");
@@ -1578,7 +1578,7 @@
           to_sbd_inj_thmss from_to_sbd_thmss Lev_0s Lev_Sucs rv_Nils rv_Conss Lev_sbd_thms
           length_Lev_thms length_Lev'_thms prefCl_Lev_thms rv_last_thmss
           set_rv_Lev_thmsss set_Lev_thmsss set_image_Lev_thmsss
-          set_map'ss coalg_set_thmss map_comp_id_thms map_cong0s map_arg_cong_thms)
+          set_mapss coalg_set_thmss map_comp_id_thms map_cong0s map_arg_cong_thms)
       |> Thm.close_derivation;
 
     val timer = time (timer "Behavioral morphism");
@@ -1617,7 +1617,7 @@
     val coalg_final_thm = Goal.prove_sorry lthy [] [] (fold_rev Logic.all As
       (HOLogic.mk_Trueprop (mk_coalg As car_finalAs str_finalAs)))
       (K (mk_coalg_final_tac m coalg_def congruent_str_final_thms equiv_LSBIS_thms
-        set_map'ss coalgT_set_thmss))
+        set_mapss coalgT_set_thmss))
       |> Thm.close_derivation;
 
     val mor_T_final_thm = Goal.prove_sorry lthy [] [] (fold_rev Logic.all As
@@ -2292,7 +2292,7 @@
               map4 (fn goal => fn cts => fn rec_0s => fn rec_Sucs =>
                 singleton (Proof_Context.export names_lthy lthy)
                   (Goal.prove_sorry lthy [] [] (HOLogic.mk_Trueprop goal)
-                    (mk_col_natural_tac cts rec_0s rec_Sucs dtor_map_thms set_map'ss))
+                    (mk_col_natural_tac cts rec_0s rec_Sucs dtor_map_thms set_mapss))
                 |> Thm.close_derivation)
               goals ctss hset_rec_0ss' hset_rec_Sucss';
           in
@@ -2360,7 +2360,7 @@
 
             val thm = singleton (Proof_Context.export names_lthy lthy)
               (Goal.prove_sorry lthy [] [] goal
-              (K (mk_mcong_tac lthy m (rtac coinduct) map_comps dtor_map_thms map_cong0s set_map'ss
+              (K (mk_mcong_tac lthy m (rtac coinduct) map_comps dtor_map_thms map_cong0s set_mapss
               set_hset_thmss set_hset_hset_thmsss)))
               |> Thm.close_derivation
           in
@@ -2396,7 +2396,7 @@
               (Logic.mk_implies (wpull_prem, coalg));
           in
             Goal.prove_sorry lthy [] [] goal (mk_coalg_thePull_tac m coalg_def map_wpull_thms
-              set_map'ss pickWP_assms_tacs)
+              set_mapss pickWP_assms_tacs)
             |> Thm.close_derivation
           end;
 
@@ -2447,7 +2447,7 @@
             val thms =
               map5 (fn j => fn goal => fn cts => fn rec_0s => fn rec_Sucs =>
                 singleton (Proof_Context.export names_lthy lthy) (Goal.prove_sorry lthy [] [] goal
-                  (mk_pick_col_tac m j cts rec_0s rec_Sucs dtor_unfold_thms set_map'ss
+                  (mk_pick_col_tac m j cts rec_0s rec_Sucs dtor_unfold_thms set_mapss
                     map_wpull_thms pickWP_assms_tacs))
                 |> Thm.close_derivation)
               ls goals ctss hset_rec_0ss' hset_rec_Sucss';
@@ -2633,7 +2633,7 @@
           in
             map2 (fn goal => fn induct =>
               Goal.prove_sorry lthy [] [] goal
-                (mk_coind_wit_tac induct dtor_unfold_thms (flat set_map'ss) wit_thms)
+                (mk_coind_wit_tac induct dtor_unfold_thms (flat set_mapss) wit_thms)
               |> Thm.close_derivation)
             goals dtor_hset_induct_thms
             |> map split_conj_thm
@@ -2707,7 +2707,7 @@
                   dtor_inject dtor_ctor set_map0s dtor_set_incls dtor_set_set_inclss))
               |> Thm.close_derivation)
             ks goals in_rels map_comps map_cong0s folded_dtor_map_thms folded_dtor_set_thmss'
-              dtor_inject_thms dtor_ctor_thms set_map'ss dtor_set_incl_thmss
+              dtor_inject_thms dtor_ctor_thms set_mapss dtor_set_incl_thmss
               dtor_set_set_incl_thmsss
           end;
 
@@ -2802,7 +2802,7 @@
               (map6 (mk_helper_coind_concl false)
               activeJphis Jzs Jz's_copy Jz's Jmap_snds zip_unfolds));
           val helper_coind_tac = mk_rel_coinduct_coind_tac m dtor_map_coinduct_thm ks map_comps
-            map_cong0s map_arg_cong_thms set_map'ss dtor_unfold_thms folded_dtor_map_thms;
+            map_cong0s map_arg_cong_thms set_mapss dtor_unfold_thms folded_dtor_map_thms;
           fun mk_helper_coind_thms vars concl =
             Goal.prove_sorry lthy [] []
               (fold_rev Logic.all (Jphis @ activeJphis @ vars @ zips)
@@ -2831,7 +2831,7 @@
               Goal.prove_sorry lthy [] []
                 (fold_rev Logic.all (Jphis @ activeJphis @ zip_zs @ zips)
                   (Logic.list_implies (helper_prems, concl)))
-                (mk_rel_coinduct_ind_tac m ks dtor_unfold_thms set_map'ss j set_induct)
+                (mk_rel_coinduct_ind_tac m ks dtor_unfold_thms set_mapss j set_induct)
               |> Thm.close_derivation
               |> split_conj_thm)
             mk_helper_ind_concls ls dtor_set_induct_thms
--- a/src/HOL/BNF/Tools/bnf_lfp.ML	Thu Aug 29 22:56:39 2013 +0200
+++ b/src/HOL/BNF/Tools/bnf_lfp.ML	Thu Aug 29 23:01:04 2013 +0200
@@ -165,7 +165,7 @@
     val map_id0s = map map_id0_of_bnf bnfs;
     val map_ids = map map_id_of_bnf bnfs;
     val map_wpulls = map map_wpull_of_bnf bnfs;
-    val set_map'ss = map set_map'_of_bnf bnfs;
+    val set_mapss = map set_map_of_bnf bnfs;
 
     val timer = time (timer "Extracted terms & thms");
 
@@ -404,7 +404,7 @@
         Goal.prove_sorry lthy [] []
           (fold_rev Logic.all (Bs @ ss @ B's @ s's @ B''s @ s''s @ fs @ gs)
              (Logic.list_implies (prems, concl)))
-          (K (mk_mor_comp_tac mor_def set_map'ss map_comp_id_thms))
+          (K (mk_mor_comp_tac mor_def set_mapss map_comp_id_thms))
         |> Thm.close_derivation
       end;
 
@@ -422,8 +422,7 @@
         Goal.prove_sorry lthy [] []
           (fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs @ inv_fs)
             (Logic.list_implies (prems, concl)))
-          (K (mk_mor_inv_tac alg_def mor_def
-            set_map'ss morE_thms map_comp_id_thms map_cong0L_thms))
+          (K (mk_mor_inv_tac alg_def mor_def set_mapss morE_thms map_comp_id_thms map_cong0L_thms))
         |> Thm.close_derivation
       end;
 
@@ -528,7 +527,7 @@
         val copy_str_thm = Goal.prove_sorry lthy [] []
           (fold_rev Logic.all (Bs @ ss @ B's @ inv_fs @ fs)
             (Logic.list_implies (all_prems, alg)))
-          (K (mk_copy_str_tac set_map'ss alg_def alg_set_thms))
+          (K (mk_copy_str_tac set_mapss alg_def alg_set_thms))
           |> Thm.close_derivation;
 
         val iso = HOLogic.mk_Trueprop
@@ -536,7 +535,7 @@
         val copy_alg_thm = Goal.prove_sorry lthy [] []
           (fold_rev Logic.all (Bs @ ss @ B's @ inv_fs @ fs)
             (Logic.list_implies (all_prems, iso)))
-          (K (mk_copy_alg_tac set_map'ss alg_set_thms mor_def iso_alt_thm copy_str_thm))
+          (K (mk_copy_alg_tac set_mapss alg_set_thms mor_def iso_alt_thm copy_str_thm))
           |> Thm.close_derivation;
 
         val ex = HOLogic.mk_Trueprop
@@ -883,7 +882,7 @@
         Goal.prove_sorry lthy [] []
           (fold_rev Logic.all (iidx :: Bs @ ss @ Asuc_fs) (Logic.list_implies (prems, concl)))
           (K (mk_mor_select_tac mor_def mor_cong_thm mor_comp_thm mor_incl_min_alg_thm alg_def
-            alg_select_thm alg_set_thms set_map'ss str_init_defs))
+            alg_select_thm alg_set_thms set_mapss str_init_defs))
         |> Thm.close_derivation
       end;
 
@@ -1335,7 +1334,7 @@
       in
         (Goal.prove_sorry lthy [] []
           (fold_rev Logic.all (phis @ Izs) goal)
-          (K (mk_ctor_induct_tac lthy m set_map'ss init_induct_thm morE_thms mor_Abs_thm
+          (K (mk_ctor_induct_tac lthy m set_mapss init_induct_thm morE_thms mor_Abs_thm
             Rep_inverses Abs_inverses Reps))
         |> Thm.close_derivation,
         rev (Term.add_tfrees goal []))
@@ -1538,7 +1537,7 @@
                 Goal.prove_sorry lthy [] [] goal
                   (K (mk_ctor_set_tac set (nth set_nats (i - 1)) (drop m set_nats)))
                 |> Thm.close_derivation)
-              set_map'ss) ls simp_goalss setss;
+              set_mapss) ls simp_goalss setss;
           in
             ctor_setss
           end;
@@ -1579,7 +1578,7 @@
                   (map4 (mk_set_map0 f) fs_maps Izs sets sets')))
                   fs setss_by_range setss_by_range';
 
-            fun mk_tac induct = mk_set_nat_tac m (rtac induct) set_map'ss ctor_map_thms;
+            fun mk_tac induct = mk_set_nat_tac m (rtac induct) set_mapss ctor_map_thms;
             val thms =
               map5 (fn goal => fn csets => fn ctor_sets => fn induct => fn i =>
                 singleton (Proof_Context.export names_lthy lthy)
@@ -1781,7 +1780,7 @@
                  ctor_inject ctor_dtor set_map0s ctor_set_incls ctor_set_set_inclss))
               |> Thm.close_derivation)
             ks goals in_rels map_comps map_cong0s folded_ctor_map_thms folded_ctor_set_thmss'
-              ctor_inject_thms ctor_dtor_thms set_map'ss ctor_set_incl_thmss
+              ctor_inject_thms ctor_dtor_thms set_mapss ctor_set_incl_thmss
               ctor_set_set_incl_thmsss
           end;
 
--- a/src/HOL/BNF/Tools/bnf_lfp_tactics.ML	Thu Aug 29 22:56:39 2013 +0200
+++ b/src/HOL/BNF/Tools/bnf_lfp_tactics.ML	Thu Aug 29 23:01:04 2013 +0200
@@ -122,39 +122,39 @@
   CONJ_WRAP' (fn thm =>
    (EVERY' [rtac ballI, rtac trans, rtac id_apply, stac thm, rtac refl])) map_ids) 1;
 
-fun mk_mor_comp_tac mor_def set_map's map_comp_ids =
+fun mk_mor_comp_tac mor_def set_maps map_comp_ids =
   let
     val fbetw_tac = EVERY' [rtac ballI, stac o_apply, etac bspec, etac bspec, atac];
-    fun mor_tac (set_map', map_comp_id) =
+    fun mor_tac (set_map, map_comp_id) =
       EVERY' [rtac ballI, stac o_apply, rtac trans,
         rtac trans, dtac rev_bspec, atac, etac arg_cong,
          REPEAT o eresolve_tac [CollectE, conjE], etac bspec, rtac CollectI] THEN'
       CONJ_WRAP' (fn thm =>
         FIRST' [rtac subset_UNIV,
           (EVERY' [rtac ord_eq_le_trans, rtac thm, rtac @{thm image_subsetI},
-            etac bspec, etac set_mp, atac])]) set_map' THEN'
+            etac bspec, etac set_mp, atac])]) set_map THEN'
       rtac (map_comp_id RS arg_cong);
   in
     (dtac (mor_def RS subst) THEN' dtac (mor_def RS subst) THEN' stac mor_def THEN'
     REPEAT o etac conjE THEN'
     rtac conjI THEN'
-    CONJ_WRAP' (K fbetw_tac) set_map's THEN'
-    CONJ_WRAP' mor_tac (set_map's ~~ map_comp_ids)) 1
+    CONJ_WRAP' (K fbetw_tac) set_maps THEN'
+    CONJ_WRAP' mor_tac (set_maps ~~ map_comp_ids)) 1
   end;
 
-fun mk_mor_inv_tac alg_def mor_def set_map's morEs map_comp_ids map_cong0Ls =
+fun mk_mor_inv_tac alg_def mor_def set_maps morEs map_comp_ids map_cong0Ls =
   let
     val fbetw_tac = EVERY' [rtac ballI, etac set_mp, etac imageI];
-    fun Collect_tac set_map' =
+    fun Collect_tac set_map =
       CONJ_WRAP' (fn thm =>
         FIRST' [rtac subset_UNIV,
           (EVERY' [rtac ord_eq_le_trans, rtac thm, rtac subset_trans,
-            etac @{thm image_mono}, atac])]) set_map';
-    fun mor_tac (set_map', ((morE, map_comp_id), map_cong0L)) =
+            etac @{thm image_mono}, atac])]) set_map;
+    fun mor_tac (set_map, ((morE, map_comp_id), map_cong0L)) =
       EVERY' [rtac ballI, ftac rev_bspec, atac,
          REPEAT o eresolve_tac [CollectE, conjE], rtac sym, rtac trans, rtac sym,
-         etac @{thm inverE}, etac bspec, rtac CollectI, Collect_tac set_map',
-         rtac trans, etac (morE RS arg_cong), rtac CollectI, Collect_tac set_map',
+         etac @{thm inverE}, etac bspec, rtac CollectI, Collect_tac set_map,
+         rtac trans, etac (morE RS arg_cong), rtac CollectI, Collect_tac set_map,
          rtac trans, rtac (map_comp_id RS arg_cong), rtac (map_cong0L RS arg_cong),
          REPEAT_DETERM_N (length morEs) o
            (EVERY' [rtac subst, rtac @{thm inver_pointfree}, etac @{thm inver_mono}, atac])];
@@ -164,8 +164,8 @@
     dtac (alg_def RS iffD1) THEN'
     REPEAT o etac conjE THEN'
     rtac conjI THEN'
-    CONJ_WRAP' (K fbetw_tac) set_map's THEN'
-    CONJ_WRAP' mor_tac (set_map's ~~ (morEs ~~ map_comp_ids ~~ map_cong0Ls))) 1
+    CONJ_WRAP' (K fbetw_tac) set_maps THEN'
+    CONJ_WRAP' mor_tac (set_maps ~~ (morEs ~~ map_comp_ids ~~ map_cong0Ls))) 1
   end;
 
 fun mk_mor_str_tac ks mor_def =
@@ -211,7 +211,7 @@
     (rtac iffI THEN' if_tac THEN' only_if_tac) 1
   end;
 
-fun mk_copy_str_tac set_map's alg_def alg_sets =
+fun mk_copy_str_tac set_maps alg_def alg_sets =
   let
     val n = length alg_sets;
     val bij_betw_inv_tac =
@@ -225,13 +225,13 @@
         EVERY' [rtac ballI, REPEAT_DETERM o eresolve_tac [CollectE, conjE], rtac set_mp,
           rtac equalityD1, etac @{thm bij_betw_imageE}, rtac imageI, etac thm,
           REPEAT_DETERM o rtac subset_UNIV, REPEAT_DETERM_N n o (set_tac thms)])
-      (set_map's ~~ alg_sets);
+      (set_maps ~~ alg_sets);
   in
     (rtac rev_mp THEN' DETERM o bij_betw_inv_tac THEN' rtac impI THEN'
     stac alg_def THEN' copy_str_tac) 1
   end;
 
-fun mk_copy_alg_tac set_map's alg_sets mor_def iso_alt copy_str =
+fun mk_copy_alg_tac set_maps alg_sets mor_def iso_alt copy_str =
   let
     val n = length alg_sets;
     val fbetw_tac = CONJ_WRAP' (K (etac @{thm bij_betwE})) alg_sets;
@@ -243,7 +243,7 @@
       CONJ_WRAP' (fn (thms, thm) =>
         EVERY' [rtac ballI, etac CollectE, etac @{thm inverE}, etac thm,
           REPEAT_DETERM o rtac subset_UNIV, REPEAT_DETERM_N n o (set_tac thms)])
-      (set_map's ~~ alg_sets);
+      (set_maps ~~ alg_sets);
   in
     (rtac (iso_alt RS iffD2) THEN'
     etac copy_str THEN' REPEAT_DETERM o atac THEN'
@@ -390,25 +390,25 @@
   EVERY' [rtac ballI, REPEAT_DETERM o eresolve_tac [CollectE, exE, conjE], hyp_subst_tac ctxt] 1 THEN
   unfold_thms_tac ctxt (Abs_inverse :: fst_snd_convs) THEN atac 1;
 
-fun mk_mor_select_tac mor_def mor_cong mor_comp mor_incl_min_alg alg_def alg_select
-    alg_sets set_map's str_init_defs =
+fun mk_mor_select_tac mor_def mor_cong mor_comp mor_incl_min_alg alg_def alg_select alg_sets
+    set_maps str_init_defs =
   let
     val n = length alg_sets;
     val fbetw_tac =
       CONJ_WRAP' (K (EVERY' [rtac ballI, etac rev_bspec, etac CollectE, atac])) alg_sets;
     val mor_tac =
       CONJ_WRAP' (fn thm => EVERY' [rtac ballI, rtac thm]) str_init_defs;
-    fun alg_epi_tac ((alg_set, str_init_def), set_map') =
+    fun alg_epi_tac ((alg_set, str_init_def), set_map) =
       EVERY' [rtac ballI, REPEAT_DETERM o eresolve_tac [CollectE, conjE], rtac CollectI,
         rtac ballI, ftac (alg_select RS bspec), stac str_init_def, etac alg_set,
         REPEAT_DETERM o FIRST' [rtac subset_UNIV,
-          EVERY' [rtac ord_eq_le_trans, resolve_tac set_map', rtac subset_trans,
+          EVERY' [rtac ord_eq_le_trans, resolve_tac set_map, rtac subset_trans,
             etac @{thm image_mono}, rtac @{thm image_Collect_subsetI}, etac bspec, atac]]];
   in
     (rtac mor_cong THEN' REPEAT_DETERM_N n o (rtac sym THEN' rtac @{thm o_id}) THEN'
     rtac (Thm.permute_prems 0 1 mor_comp) THEN' etac (Thm.permute_prems 0 1 mor_comp) THEN'
     stac mor_def THEN' rtac conjI THEN' fbetw_tac THEN' mor_tac THEN' rtac mor_incl_min_alg THEN'
-    stac alg_def THEN' CONJ_WRAP' alg_epi_tac ((alg_sets ~~ str_init_defs) ~~ set_map's)) 1
+    stac alg_def THEN' CONJ_WRAP' alg_epi_tac ((alg_sets ~~ str_init_defs) ~~ set_maps)) 1
   end;
 
 fun mk_init_ex_mor_tac Abs_inverse copy_alg_ex alg_min_alg card_of_min_algs
@@ -534,21 +534,21 @@
     (rec_defs @ map (fn thm => thm RS @{thm convol_expand_snd'}) fst_recs) THEN
   etac fold_unique_mor 1;
 
-fun mk_ctor_induct_tac ctxt m set_map'ss init_induct morEs mor_Abs Rep_invs Abs_invs Reps =
+fun mk_ctor_induct_tac ctxt m set_mapss init_induct morEs mor_Abs Rep_invs Abs_invs Reps =
   let
-    val n = length set_map'ss;
+    val n = length set_mapss;
     val ks = 1 upto n;
 
-    fun mk_IH_tac Rep_inv Abs_inv set_map' =
+    fun mk_IH_tac Rep_inv Abs_inv set_map =
       DETERM o EVERY' [dtac meta_mp, rtac (Rep_inv RS arg_cong RS subst), etac bspec,
-        dtac set_rev_mp, rtac equalityD1, rtac set_map', etac imageE,
+        dtac set_rev_mp, rtac equalityD1, rtac set_map, etac imageE,
         hyp_subst_tac ctxt, rtac (Abs_inv RS ssubst), etac set_mp, atac, atac];
 
-    fun mk_closed_tac (k, (morE, set_map's)) =
+    fun mk_closed_tac (k, (morE, set_maps)) =
       EVERY' [select_prem_tac n (dtac asm_rl) k, rtac ballI, rtac impI,
         rtac (mor_Abs RS morE RS arg_cong RS ssubst), atac,
         REPEAT_DETERM o eresolve_tac [CollectE, conjE], dtac @{thm meta_spec},
-        EVERY' (map3 mk_IH_tac Rep_invs Abs_invs (drop m set_map's)), atac];
+        EVERY' (map3 mk_IH_tac Rep_invs Abs_invs (drop m set_maps)), atac];
 
     fun mk_induct_tac (Rep, Rep_inv) =
       EVERY' [rtac (Rep_inv RS arg_cong RS subst), etac (Rep RSN (2, bspec))];
@@ -556,7 +556,7 @@
     (rtac mp THEN' rtac impI THEN'
     DETERM o CONJ_WRAP_GEN' (etac conjE THEN' rtac conjI) mk_induct_tac (Reps ~~ Rep_invs) THEN'
     rtac init_induct THEN'
-    DETERM o CONJ_WRAP' mk_closed_tac (ks ~~ (morEs ~~ set_map'ss))) 1
+    DETERM o CONJ_WRAP' mk_closed_tac (ks ~~ (morEs ~~ set_mapss))) 1
   end;
 
 fun mk_ctor_induct2_tac cTs cts ctor_induct weak_ctor_inducts {context = ctxt, prems = _} =
@@ -592,19 +592,19 @@
 fun mk_set_tac foldx = EVERY' [rtac ext, rtac trans, rtac o_apply,
   rtac trans, rtac foldx, rtac sym, rtac o_apply] 1;
 
-fun mk_ctor_set_tac set set_map' set_map's =
+fun mk_ctor_set_tac set set_map set_maps =
   let
-    val n = length set_map's;
+    val n = length set_maps;
     fun mk_UN thm = rtac (thm RS @{thm arg_cong[of _ _ Union]} RS trans) THEN'
       rtac @{thm Union_image_eq};
   in
     EVERY' [rtac (set RS @{thm comp_eq_dest} RS trans), rtac Un_cong,
-      rtac (trans OF [set_map', trans_fun_cong_image_id_id_apply]),
+      rtac (trans OF [set_map, trans_fun_cong_image_id_id_apply]),
       REPEAT_DETERM_N (n - 1) o rtac Un_cong,
-      EVERY' (map mk_UN set_map's)] 1
+      EVERY' (map mk_UN set_maps)] 1
   end;
 
-fun mk_set_nat_tac m induct_tac set_map'ss
+fun mk_set_nat_tac m induct_tac set_mapss
     ctor_maps csets ctor_sets i {context = ctxt, prems = _} =
   let
     val n = length ctor_maps;
@@ -621,7 +621,7 @@
         REPEAT_DETERM_N (n - 1) o EVERY' (map rtac [trans, @{thm image_Un}, Un_cong]),
         EVERY' (map useIH (drop m set_nats))];
   in
-    (induct_tac THEN' EVERY' (map4 mk_set_nat csets ctor_maps ctor_sets set_map'ss)) 1
+    (induct_tac THEN' EVERY' (map4 mk_set_nat csets ctor_maps ctor_sets set_mapss)) 1
   end;
 
 fun mk_set_bd_tac m induct_tac bd_Cinfinite set_bdss ctor_sets i {context = ctxt, prems = _} =