src/HOL/Tools/BNF/bnf_fp_def_sugar.ML

      map_sels: thm list,
      rel_injects: thm list,
      rel_distincts: thm list,
      rel_sels: thm list,
      rel_intros: thm list,
-     rel_cases: thm list}
+     rel_cases: thm list,
+     set_thms: thm list}
 
   type fp_co_induct_sugar =
     {co_rec: term,
      common_co_inducts: thm list,
      co_inducts: thm list,

    map_sels: thm list,
    rel_injects: thm list,
    rel_distincts: thm list,
    rel_sels: thm list,
    rel_intros: thm list,
-   rel_cases: thm list};
+   rel_cases: thm list,
+   set_thms: thm list};
 
 type fp_co_induct_sugar =
   {co_rec: term,
    common_co_inducts: thm list,
    co_inducts: thm list,

    fp_ctr_sugar: fp_ctr_sugar,
    fp_bnf_sugar: fp_bnf_sugar,
    fp_co_induct_sugar: fp_co_induct_sugar};
 
 fun morph_fp_bnf_sugar phi ({map_thms, map_disc_iffs, map_sels, rel_injects, rel_distincts,
-    rel_sels, rel_intros, rel_cases} : fp_bnf_sugar) =
+    rel_sels, rel_intros, rel_cases, set_thms} : fp_bnf_sugar) =
   {map_thms = map (Morphism.thm phi) map_thms,
    map_disc_iffs = map (Morphism.thm phi) map_disc_iffs,
    map_sels = map (Morphism.thm phi) map_sels,
    rel_injects = map (Morphism.thm phi) rel_injects,
    rel_distincts = map (Morphism.thm phi) rel_distincts,
    rel_sels = map (Morphism.thm phi) rel_sels,
    rel_intros = map (Morphism.thm phi) rel_intros,
-   rel_cases = map (Morphism.thm phi) rel_cases};
+   rel_cases = map (Morphism.thm phi) rel_cases,
+   set_thms = map (Morphism.thm phi) set_thms};
 
 fun morph_fp_co_induct_sugar phi ({co_rec, common_co_inducts, co_inducts, co_rec_def, co_rec_thms,
     co_rec_discs, co_rec_selss} : fp_co_induct_sugar) =
   {co_rec = Morphism.term phi co_rec,
    common_co_inducts = map (Morphism.thm phi) common_co_inducts,

   register_fp_sugars_raw fp_sugars #> interpret_fp_sugars plugins fp_sugars;
 
 fun interpret_bnfs_register_fp_sugars plugins Ts BTs Xs fp pre_bnfs absT_infos fp_nesting_bnfs
     live_nesting_bnfs fp_res ctrXs_Tsss ctr_defss ctr_sugars co_recs co_rec_defs map_thmss
     common_co_inducts co_inductss co_rec_thmss co_rec_discss co_rec_selsss rel_injectss
-    rel_distinctss map_disc_iffss map_selss rel_selss rel_intross rel_casess noted =
+    rel_distinctss map_disc_iffss map_selss rel_selss rel_intross rel_casess set_thmss noted =
   let
     val fp_sugars =
       map_index (fn (kk, T) =>
         {T = T, BT = nth BTs kk, X = nth Xs kk, fp = fp, fp_res = fp_res, fp_res_index = kk,
          pre_bnf = nth pre_bnfs kk, absT_info = nth absT_infos kk,

             map_sels = nth map_selss kk,
             rel_injects = nth rel_injectss kk,
             rel_distincts = nth rel_distinctss kk,
             rel_sels = nth rel_selss kk,
             rel_intros = nth rel_intross kk,
-            rel_cases = nth rel_casess kk},
+            rel_cases = nth rel_casess kk,
+            set_thms = nth set_thmss kk},
          fp_co_induct_sugar =
            {co_rec = nth co_recs kk,
             common_co_inducts = common_co_inducts,
             co_inducts = nth co_inductss kk,
             co_rec_def = nth co_rec_defs kk,

         map subst rel_inject_thms,
         map subst rel_distinct_thms,
         map subst rel_sel_thms,
         map subst rel_intro_thms,
         [subst rel_cases_thm],
-        map (map subst) set0_thmss), lthy')
+        map subst set_thms), lthy')
     end;
 
 type lfp_sugar_thms = (thm list * thm * Token.src list) * (thm list list * Token.src list);
 
 fun morph_lfp_sugar_thms phi ((inducts, induct, induct_attrs), (recss, rec_attrs)) =

       fold_map I wrap_one_etc lthy
       |>> apsnd split_list o apfst (apsnd split_list4 o apfst split_list9 o split_list)
         o split_list;
 
     fun mk_simp_thms ({injects, distincts, case_thms, ...} : ctr_sugar) co_recs map_thms rel_injects
-        rel_distincts setss =
-      injects @ distincts @ case_thms @ co_recs @ map_thms @ rel_injects @ rel_distincts @ flat setss;
+        rel_distincts set_thmss =
+      injects @ distincts @ case_thms @ co_recs @ map_thms @ rel_injects @ rel_distincts @
+      set_thmss;
 
     fun mk_co_rec_transfer_goals lthy co_recs =
       let
         val liveAsBs = filter (op <>) (As ~~ Bs);
         val B_ify = Term.subst_atomic_types (liveAsBs @ (Cs ~~ Es));

         |> map Thm.close_derivation
       end;
 
     fun derive_note_induct_recs_thms_for_types
         ((((map_thmss, map_disc_iffss, map_selss, rel_injectss, rel_distinctss, rel_selss,
-            rel_intross, rel_casess, setss),
+            rel_intross, rel_casess, set_thmss),
            (ctrss, _, ctr_defss, ctr_sugars)),
           (recs, rec_defs)), lthy) =
       let
         val ((induct_thms, induct_thm, induct_attrs), (rec_thmss, rec_attrs)) =
           derive_induct_recs_thms_for_types plugins pre_bnfs recs_args_types xtor_co_induct

               ((map single rel_induct_thms, single common_rel_induct_thm),
                (rel_induct_attrs, rel_induct_attrs))
             end;
 
         val simp_thmss =
-          map6 mk_simp_thms ctr_sugars rec_thmss map_thmss rel_injectss rel_distinctss setss;
+          map6 mk_simp_thms ctr_sugars rec_thmss map_thmss rel_injectss rel_distinctss set_thmss;
 
         val common_notes =
           (if nn > 1 then
              [(inductN, [induct_thm], K induct_attrs),
               (rel_inductN, common_rel_induct_thms, K common_rel_induct_attrs)]

         (* for "datatype_realizer.ML": *)
         |>> name_noted_thms
           (fst (dest_Type (hd fpTs)) ^ (implode (map (prefix "_") (tl fp_b_names)))) inductN
         |-> interpret_bnfs_register_fp_sugars plugins fpTs fpBTs Xs Least_FP pre_bnfs absT_infos
           fp_nesting_bnfs live_nesting_bnfs fp_res ctrXs_Tsss ctr_defss ctr_sugars recs rec_defs
-          map_thmss [induct_thm] (map single induct_thms) rec_thmss (replicate nn []) (replicate nn [])
-          rel_injectss rel_distinctss map_disc_iffss map_selss rel_selss rel_intross rel_casess
+          map_thmss [induct_thm] (map single induct_thms) rec_thmss (replicate nn [])
+          (replicate nn []) rel_injectss rel_distinctss map_disc_iffss map_selss rel_selss
+          rel_intross rel_casess set_thmss
       end;
 
     fun derive_corec_transfer_thms lthy corecs corec_defs =
       let
         val (Rs, Ss, goals, names_lthy) = mk_co_rec_transfer_goals lthy corecs;

         |> map Thm.close_derivation
       end;
 
     fun derive_note_coinduct_corecs_thms_for_types
         ((((map_thmss, map_disc_iffss, map_selss, rel_injectss, rel_distinctss, rel_selss,
-            rel_intross, rel_casess, setss),
+            rel_intross, rel_casess, set_thmss),
            (_, _, ctr_defss, ctr_sugars)),
           (corecs, corec_defs)), lthy) =
       let
         val (([(coinduct_thms, coinduct_thm), (coinduct_strong_thms, coinduct_strong_thm)],
               (coinduct_attrs, common_coinduct_attrs)),

           |> split_list;
 
         val simp_thmss =
           map6 mk_simp_thms ctr_sugars
             (map3 flat_corec_thms corec_disc_thmss corec_disc_iff_thmss corec_sel_thmss)
-            map_thmss rel_injectss rel_distinctss setss;
+            map_thmss rel_injectss rel_distinctss set_thmss;
 
         val common_notes =
           (set_inductN, set_induct_thms, nth set_induct_attrss) ::
           (if nn > 1 then
             [(coinductN, [coinduct_thm], K common_coinduct_attrs),

         |-> interpret_bnfs_register_fp_sugars plugins fpTs fpBTs Xs Greatest_FP pre_bnfs absT_infos
           fp_nesting_bnfs live_nesting_bnfs fp_res ctrXs_Tsss ctr_defss ctr_sugars corecs corec_defs
           map_thmss [coinduct_thm, coinduct_strong_thm]
           (transpose [coinduct_thms, coinduct_strong_thms]) corec_thmss corec_disc_thmss
           corec_sel_thmsss rel_injectss rel_distinctss map_disc_iffss map_selss rel_selss
-          rel_intross rel_casess
+          rel_intross rel_casess set_thmss
       end;
 
     val lthy'' = lthy'
       |> live > 0 ? fold2 (fn Type (s, _) => fn bnf => register_bnf_raw s bnf) fpTs fp_bnfs
       |> fold_map define_ctrs_dtrs_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ ctors ~~ dtors ~~