src/HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML

   val mk_coiter_like_tac: thm list -> thm list -> thm -> thm -> thm -> Proof.context -> tactic
   val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic
   val mk_fld_iff_unf_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm ->
     tactic
   val mk_half_distinct_tac: Proof.context -> thm -> thm list -> tactic
-  val mk_induct_tac: Proof.context -> int list -> int list list -> int list list -> thm list ->
-    thm -> thm list list -> thm list -> tactic
+  val mk_induct_tac: Proof.context -> int list -> int list list -> (int * int) list list list ->
+    thm list -> thm -> thm list -> thm list list -> tactic
   val mk_inject_tac: Proof.context -> thm -> thm -> tactic
   val mk_iter_like_tac: thm list -> thm list -> thm list -> thm -> thm -> Proof.context -> tactic
 end;
 
 structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS =

    delay them. *)
 val induct_prem_prem_thms_delayed =
   @{thms fsts_def[abs_def] snds_def[abs_def] sum_setl_def[abs_def] sum_setr_def[abs_def]};
 
 (* TODO: Get rid of the "blast_tac" *)
-fun mk_induct_discharge_prem_prems_tac ctxt r pre_set_defs set_natural's =
-  EVERY' (maps (fn i =>
-    [dtac meta_spec, rotate_tac ~1, etac meta_mp,
-     SELECT_GOAL (Local_Defs.unfold_tac ctxt pre_set_defs),
+fun mk_induct_discharge_prem_prems_tac ctxt ppis set_natural's pre_set_defs =
+  EVERY' (maps (fn (pp, i) =>
+    [(* ### select_prem_tac pp (dtac meta_spec) i, *) dtac meta_spec, rotate_tac ~1, etac meta_mp,
+     SELECT_GOAL (Local_Defs.unfold_tac ctxt pre_set_defs), (* ### why on a line of its own? *)
      SELECT_GOAL (Local_Defs.unfold_tac ctxt (set_natural's @ induct_prem_prem_thms)),
      SELECT_GOAL (Local_Defs.unfold_tac ctxt
        (induct_prem_prem_thms_delayed @ induct_prem_prem_thms)),
-     TRY o rtac (mk_UnIN r i), (* FIXME: crude hack, doesn't work in the general case *)
+     TRY o rtac (mk_UnIN pp i), (*#####*)
      atac ORELSE'
      rtac @{thm singletonI} ORELSE'
      (REPEAT_DETERM o (SELECT_GOAL (Local_Defs.unfold_tac ctxt @{thms Union_iff bex_simps(6)}) THEN'
           etac @{thm induct_set_step}) THEN'
-        (atac ORELSE' blast_tac ctxt))]) (r downto 1)) 1;
+      (atac ORELSE' blast_tac ctxt))]) (rev ppis)) 1;
 
-fun mk_induct_discharge_prem_tac ctxt n m k r pre_set_defs set_natural's =
+fun mk_induct_discharge_prem_tac ctxt n set_natural's pre_set_defs m k ppis =
   EVERY [mk_induct_prepare_prem_tac n m k,
-    mk_induct_prepare_prem_prems_tac r, atac 1,
-    mk_induct_discharge_prem_prems_tac ctxt r pre_set_defs set_natural's];
+    mk_induct_prepare_prem_prems_tac (length ppis), atac 1,
+    mk_induct_discharge_prem_prems_tac ctxt ppis set_natural's pre_set_defs];
 
-fun mk_induct_tac ctxt ns mss rss ctr_defs fld_induct' pre_set_defss set_natural's =
+fun mk_induct_tac ctxt ns mss ppisss ctr_defs fld_induct' set_natural's pre_set_defss =
   let val n = Integer.sum ns in
     mk_induct_prelude_tac ctxt ctr_defs fld_induct' THEN
-    EVERY (map4 (fn pre_set_defs =>
-        EVERY ooo map3 (fn m => fn k => fn r =>
-            mk_induct_discharge_prem_tac ctxt n m k r pre_set_defs set_natural's))
-      pre_set_defss mss (unflat mss (1 upto n)) rss)
+    EVERY (map4 (EVERY oooo map3 o mk_induct_discharge_prem_tac ctxt n set_natural's)
+      pre_set_defss mss (unflat mss (1 upto n)) ppisss)
   end;
 
 end;