renamed confusing variable names

--- a/src/HOL/Tools/BNF/bnf_fp_def_sugar.ML	Tue Dec 20 16:18:56 2016 +0100
+++ b/src/HOL/Tools/BNF/bnf_fp_def_sugar.ML	Wed Dec 21 11:14:37 2016 +0100
@@ -1721,7 +1721,7 @@
   end;
 
 fun derive_induct_recs_thms_for_types plugins pre_bnfs rec_args_typess ctor_induct ctor_rec_thms
-    live_nesting_bnfs fp_nesting_bnfs fpTs Cs Xs ctrXs_Tsss fp_abs_inverses pre_type_definitions
+    live_nesting_bnfs fp_nesting_bnfs fpTs Cs Xs ctrXs_Tsss pre_abs_inverses pre_type_definitions
     abs_inverses ctrss ctr_defss recs rec_defs lthy =
   let
     val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
@@ -1758,14 +1758,13 @@
           Library.foldr (Logic.list_implies o apfst (map (finish_induct_prem lthy nn ps)))
             (raw_premss, concl);
         val vars = Variable.add_free_names lthy goal [];
-
         val kksss = map (map (map (fst o snd) o #2)) raw_premss;
 
         val ctor_induct' = ctor_induct OF (map2 mk_absumprodE pre_type_definitions mss);
 
         val thm =
           Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, ...} =>
-            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' fp_abs_inverses
+            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' pre_abs_inverses
               abs_inverses fp_nesting_set_maps pre_set_defss)
           |> Thm.close_derivation;
       in
@@ -1805,7 +1804,7 @@
 
         val tacss = @{map 4} (map ooo
               mk_rec_tac pre_map_defs (fp_nesting_map_ident0s @ live_nesting_map_ident0s) rec_defs)
-            ctor_rec_thms fp_abs_inverses abs_inverses ctr_defss;
+            ctor_rec_thms pre_abs_inverses abs_inverses ctr_defss;
 
         fun prove goal tac =
           Goal.prove_sorry lthy [] [] goal (tac o #context)
@@ -2035,7 +2034,7 @@
   end;
 
 fun derive_coinduct_thms_for_types strong alter_r pre_bnfs dtor_coinduct dtor_ctors
-    live_nesting_bnfs fpTs Xs ctrXs_Tsss ns fp_abs_inverses abs_inverses mk_vimage2p ctr_defss
+    live_nesting_bnfs fpTs Xs ctrXs_Tsss ns pre_abs_inverses abs_inverses mk_vimage2p ctr_defss
     (ctr_sugars : ctr_sugar list) ctxt =
   let
     val nn = length pre_bnfs;
@@ -2108,7 +2107,7 @@
     fun prove dtor_coinduct' goal =
       Variable.add_free_names ctxt goal []
       |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, ...} =>
-        mk_coinduct_tac ctxt live_nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs fp_abs_inverses
+        mk_coinduct_tac ctxt live_nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs pre_abs_inverses
           abs_inverses dtor_ctors exhausts ctr_defss disc_thmsss sel_thmsss))
       |> Thm.close_derivation;
 
@@ -2125,7 +2124,7 @@
 
 fun derive_coinduct_corecs_thms_for_types pre_bnfs (x, cs, cpss, (((pgss, _, _, _), cqgsss), _))
     dtor_coinduct dtor_injects dtor_ctors dtor_corec_thms live_nesting_bnfs fpTs Cs Xs ctrXs_Tsss
-    kss mss ns fp_abs_inverses abs_inverses mk_vimage2p ctr_defss (ctr_sugars : ctr_sugar list)
+    kss mss ns pre_abs_inverses abs_inverses mk_vimage2p ctr_defss (ctr_sugars : ctr_sugar list)
     corecs corec_defs ctxt =
   let
     fun mk_ctor_dtor_corec_thm dtor_inject dtor_ctor corec =
@@ -2147,7 +2146,7 @@
     val sel_thmsss = map #sel_thmss ctr_sugars;
 
     val coinduct_thms_pairs = derive_coinduct_thms_for_types true I pre_bnfs dtor_coinduct
-      dtor_ctors live_nesting_bnfs fpTs Xs ctrXs_Tsss ns fp_abs_inverses abs_inverses mk_vimage2p
+      dtor_ctors live_nesting_bnfs fpTs Xs ctrXs_Tsss ns pre_abs_inverses abs_inverses mk_vimage2p
       ctr_defss ctr_sugars ctxt;
 
     fun mk_maybe_not pos = not pos ? HOLogic.mk_not;

--- a/src/HOL/Tools/BNF/bnf_fp_def_sugar_tactics.ML	Tue Dec 20 16:18:56 2016 +0100
+++ b/src/HOL/Tools/BNF/bnf_fp_def_sugar_tactics.ML	Wed Dec 21 11:14:37 2016 +0100
@@ -177,10 +177,10 @@
         rec_o_map_simps) ctxt))
   end;
 
-fun mk_rec_tac pre_map_defs map_ident0s rec_defs ctor_rec fp_abs_inverse abs_inverse ctr_def ctxt =
+fun mk_rec_tac pre_map_defs map_ident0s rec_defs ctor_rec pre_abs_inverse abs_inverse ctr_def ctxt =
   HEADGOAL ((if is_def_looping ctr_def then subst_tac ctxt NONE
     else SELECT_GOAL o unfold_thms_tac ctxt) [ctr_def]) THEN
-  unfold_thms_tac ctxt (ctor_rec :: fp_abs_inverse :: abs_inverse :: rec_defs @
+  unfold_thms_tac ctxt (ctor_rec :: pre_abs_inverse :: abs_inverse :: rec_defs @
     pre_map_defs @ map_ident0s @ rec_unfold_thms) THEN HEADGOAL (rtac ctxt refl);
 
 fun mk_rec_transfer_tac ctxt nn ns actives passives xssss rec_defs ctor_rec_transfers rel_pre_T_defs
@@ -314,15 +314,15 @@
     resolve_tac ctxt @{thms disjI1 disjI2}) THEN'
   (rtac ctxt refl ORELSE' assume_tac ctxt ORELSE' rtac ctxt @{thm singletonI});
 
-fun mk_induct_leverage_prem_prems_tac ctxt nn kks fp_abs_inverses abs_inverses set_maps
+fun mk_induct_leverage_prem_prems_tac ctxt nn kks pre_abs_inverses abs_inverses set_maps
     pre_set_defs =
   HEADGOAL (EVERY' (maps (fn kk => [select_prem_tac ctxt nn (dtac ctxt meta_spec) kk,
     etac ctxt meta_mp,
-    SELECT_GOAL (unfold_thms_tac ctxt (pre_set_defs @ fp_abs_inverses @ abs_inverses @ set_maps @
+    SELECT_GOAL (unfold_thms_tac ctxt (pre_set_defs @ pre_abs_inverses @ abs_inverses @ set_maps @
       sumprod_thms_set)),
     solve_prem_prem_tac ctxt]) (rev kks)));
 
-fun mk_induct_discharge_prem_tac ctxt nn n fp_abs_inverses abs_inverses set_maps pre_set_defs m k
+fun mk_induct_discharge_prem_tac ctxt nn n pre_abs_inverses abs_inverses set_maps pre_set_defs m k
     kks =
   let val r = length kks in
     HEADGOAL (EVERY' [select_prem_tac ctxt n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac ctxt,
@@ -330,11 +330,11 @@
     EVERY [REPEAT_DETERM_N r
         (HEADGOAL (rotate_tac ~1 THEN' dtac ctxt meta_mp THEN' rotate_tac 1) THEN prefer_tac 2),
       if r > 0 then ALLGOALS (Goal.norm_hhf_tac ctxt) else all_tac, HEADGOAL (assume_tac ctxt),
-      mk_induct_leverage_prem_prems_tac ctxt nn kks fp_abs_inverses abs_inverses set_maps
+      mk_induct_leverage_prem_prems_tac ctxt nn kks pre_abs_inverses abs_inverses set_maps
         pre_set_defs]
   end;
 
-fun mk_induct_tac ctxt nn ns mss kkss ctr_defs ctor_induct' fp_abs_inverses abs_inverses set_maps
+fun mk_induct_tac ctxt nn ns mss kksss ctr_defs ctor_induct' pre_abs_inverses abs_inverses set_maps
     pre_set_defss =
   let val n = Integer.sum ns in
     (if exists is_def_looping ctr_defs then
@@ -343,17 +343,17 @@
        unfold_thms_tac ctxt ctr_defs) THEN
     HEADGOAL (rtac ctxt ctor_induct') THEN co_induct_inst_as_projs_tac ctxt 0 THEN
     EVERY (@{map 4} (EVERY oooo @{map 3} o
-        mk_induct_discharge_prem_tac ctxt nn n fp_abs_inverses abs_inverses set_maps)
-      pre_set_defss mss (unflat mss (1 upto n)) kkss)
+        mk_induct_discharge_prem_tac ctxt nn n pre_abs_inverses abs_inverses set_maps)
+      pre_set_defss mss (unflat mss (1 upto n)) kksss)
   end;
 
-fun mk_coinduct_same_ctr_tac ctxt rel_eqs pre_rel_def fp_abs_inverse abs_inverse dtor_ctor ctr_def
+fun mk_coinduct_same_ctr_tac ctxt rel_eqs pre_rel_def pre_abs_inverse abs_inverse dtor_ctor ctr_def
     discs sels =
   hyp_subst_tac ctxt THEN'
   CONVERSION (hhf_concl_conv
     (Conv.top_conv (K (Conv.try_conv (Conv.rewr_conv ctr_def))) ctxt) ctxt) THEN'
   SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: dtor_ctor :: sels)) THEN'
-  SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: fp_abs_inverse :: abs_inverse :: dtor_ctor ::
+  SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: pre_abs_inverse :: abs_inverse :: dtor_ctor ::
     sels @ sumprod_thms_rel @ @{thms o_apply vimage2p_def})) THEN'
   (assume_tac ctxt ORELSE' REPEAT o etac ctxt conjE THEN'
      full_simp_tac (ss_only (no_refl discs @ rel_eqs @ more_simp_thms) ctxt) THEN'
@@ -369,7 +369,7 @@
     full_simp_tac (ss_only (refl :: no_refl discs'' @ basic_simp_thms) ctxt)
   end;
 
-fun mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn kk n pre_rel_def fp_abs_inverse abs_inverse
+fun mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn kk n pre_rel_def pre_abs_inverse abs_inverse
     dtor_ctor exhaust ctr_defs discss selss =
   let val ks = 1 upto n in
     EVERY' ([rtac ctxt allI, rtac ctxt allI, rtac ctxt impI,
@@ -380,18 +380,18 @@
         EVERY' ([rtac ctxt exhaust, K (co_induct_inst_as_projs_tac ctxt 1)] @
           map2 (fn k' => fn discs' =>
             if k' = k then
-              mk_coinduct_same_ctr_tac ctxt rel_eqs' pre_rel_def fp_abs_inverse abs_inverse
+              mk_coinduct_same_ctr_tac ctxt rel_eqs' pre_rel_def pre_abs_inverse abs_inverse
                 dtor_ctor ctr_def discs sels
             else
               mk_coinduct_distinct_ctrs_tac ctxt discs discs') ks discss)) ks ctr_defs discss selss)
   end;
 
-fun mk_coinduct_tac ctxt rel_eqs' nn ns dtor_coinduct' pre_rel_defs fp_abs_inverses abs_inverses
+fun mk_coinduct_tac ctxt rel_eqs' nn ns dtor_coinduct' pre_rel_defs pre_abs_inverses abs_inverses
     dtor_ctors exhausts ctr_defss discsss selsss =
   HEADGOAL (rtac ctxt dtor_coinduct' THEN'
     EVERY' (@{map 10} (mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn)
-      (1 upto nn) ns pre_rel_defs fp_abs_inverses abs_inverses dtor_ctors exhausts ctr_defss discsss
-      selsss));
+      (1 upto nn) ns pre_rel_defs pre_abs_inverses abs_inverses dtor_ctors exhausts ctr_defss
+      discsss selsss));
 
 fun mk_map_tac ctxt abs_inverses pre_map_def map_ctor live_nesting_map_id0s ctr_defs'
     extra_unfolds =