# HG changeset patch
# User Cezary Kaliszyk <kaliszyk@in.tum.de>
# Date 1269876737 -7200
# Node ID b5141d1ab24f36f6ff4a75d97d62442375f3e07a
# Parent  2dca07aca28745801079dc53d9727cc100b16215
Initial renaming

diff -r 2dca07aca287 -r b5141d1ab24f Nominal/ExCoreHaskell.thy
--- a/Nominal/ExCoreHaskell.thy	Mon Mar 29 17:14:02 2010 +0200
+++ b/Nominal/ExCoreHaskell.thy	Mon Mar 29 17:32:17 2010 +0200
@@ -64,69 +64,69 @@
   ANil
 | ACons p::"pat" t::"trm" "assoc_lst" bind "bv p" in t
 and pat =
-  Kpat "string" "tvtk_lst" "tvck_lst" "vt_lst"
-and vt_lst =
-  VTNil
-| VTCons "var" "ty" "vt_lst"
-and tvtk_lst =
-  TVTKNil
-| TVTKCons "tvar" "tkind" "tvtk_lst"
-and tvck_lst =
-  TVCKNil
-| TVCKCons "cvar" "ckind" "tvck_lst"
+  Kpat "string" "tvars" "cvars" "vars"
+and vars =
+  VsNil
+| VsCons "var" "ty" "vars"
+and tvars =
+  TvsNil
+| TvsCons "tvar" "tkind" "tvars"
+and cvars =
+  CvsNil
+| CvsCons "cvar" "ckind" "cvars"
 binder
     bv :: "pat \<Rightarrow> atom list"
-and bv_vt :: "vt_lst \<Rightarrow> atom list"
-and bv_tvtk :: "tvtk_lst \<Rightarrow> atom list"
-and bv_tvck :: "tvck_lst \<Rightarrow> atom list"
+and bv_vs :: "vars \<Rightarrow> atom list"
+and bv_tvs :: "tvars \<Rightarrow> atom list"
+and bv_cvs :: "cvars \<Rightarrow> atom list"
 where
-  "bv (K s tvts tvcs vs) = append (bv_tvtk tvts) (append (bv_tvck tvcs) (bv_vt vs))"
-| "bv_vt VTNil = []"
-| "bv_vt (VTCons v k t) = (atom v) # bv_vt t"
-| "bv_tvtk TVTKNil = []"
-| "bv_tvtk (TVTKCons v k t) = (atom v) # bv_tvtk t"
-| "bv_tvck TVCKNil = []"
-| "bv_tvck (TVCKCons v k t) = (atom v) # bv_tvck t"
+  "bv (Kpat s tvts tvcs vs) = append (bv_tvs tvts) (append (bv_cvs tvcs) (bv_vs vs))"
+| "bv_vs VsNil = []"
+| "bv_vs (VsCons v k t) = (atom v) # bv_vs t"
+| "bv_tvs TvsNil = []"
+| "bv_tvs (TvsCons v k t) = (atom v) # bv_tvs t"
+| "bv_cvs CvsNil = []"
+| "bv_cvs (CvsCons v k t) = (atom v) # bv_cvs t"
 
-lemmas fv_supp=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vt_lst_tvtk_lst_tvck_lst.supp(1-9,11,13,15)
-lemmas supp=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vt_lst_tvtk_lst_tvck_lst.fv[simplified fv_supp]
-lemmas perm=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vt_lst_tvtk_lst_tvck_lst.perm
-lemmas eq_iff=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vt_lst_tvtk_lst_tvck_lst.eq_iff
-lemmas inducts=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vt_lst_tvtk_lst_tvck_lst.inducts
+lemmas fv_supp=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.supp(1-9,11,13,15)
+lemmas supp=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.fv[simplified fv_supp]
+lemmas perm=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.perm
+lemmas eq_iff=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.eq_iff
+lemmas inducts=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.inducts
 
-lemmas alpha_inducts=alpha_tkind_raw_alpha_ckind_raw_alpha_ty_raw_alpha_ty_lst_raw_alpha_co_raw_alpha_co_lst_raw_alpha_trm_raw_alpha_assoc_lst_raw_alpha_pat_raw_alpha_vt_lst_raw_alpha_tvtk_lst_raw_alpha_tvck_lst_raw_alpha_bv_raw_alpha_bv_vt_raw_alpha_bv_tvtk_raw_alpha_bv_tvck_raw.inducts
-lemmas alpha_intros=alpha_tkind_raw_alpha_ckind_raw_alpha_ty_raw_alpha_ty_lst_raw_alpha_co_raw_alpha_co_lst_raw_alpha_trm_raw_alpha_assoc_lst_raw_alpha_pat_raw_alpha_vt_lst_raw_alpha_tvtk_lst_raw_alpha_tvck_lst_raw_alpha_bv_raw_alpha_bv_vt_raw_alpha_bv_tvtk_raw_alpha_bv_tvck_raw.intros
+lemmas alpha_inducts=alpha_tkind_raw_alpha_ckind_raw_alpha_ty_raw_alpha_ty_lst_raw_alpha_co_raw_alpha_co_lst_raw_alpha_trm_raw_alpha_assoc_lst_raw_alpha_pat_raw_alpha_vars_raw_alpha_tvars_raw_alpha_cvars_raw_alpha_bv_raw_alpha_bv_vs_raw_alpha_bv_tvs_raw_alpha_bv_cvs_raw.inducts
+lemmas alpha_intros=alpha_tkind_raw_alpha_ckind_raw_alpha_ty_raw_alpha_ty_lst_raw_alpha_co_raw_alpha_co_lst_raw_alpha_trm_raw_alpha_assoc_lst_raw_alpha_pat_raw_alpha_vars_raw_alpha_tvars_raw_alpha_cvars_raw_alpha_bv_raw_alpha_bv_vs_raw_alpha_bv_tvs_raw_alpha_bv_cvs_raw.intros
 
 lemma fresh_star_minus_perm: "as \<sharp>* - p = as \<sharp>* (p :: perm)"
   unfolding fresh_star_def Ball_def
   by auto (simp_all add: fresh_minus_perm)
 
-primrec permute_bv_vt_raw
-where "permute_bv_vt_raw p VTNil_raw = VTNil_raw"
-|     "permute_bv_vt_raw p (VTCons_raw v t l) = VTCons_raw (p \<bullet> v) t (permute_bv_vt_raw p l)"
-primrec permute_bv_tvck_raw
-where "permute_bv_tvck_raw p TVCKNil_raw = TVCKNil_raw"
-|     "permute_bv_tvck_raw p (TVCKCons_raw v t l) = TVCKCons_raw (p \<bullet> v) t (permute_bv_tvck_raw p l)"
-primrec permute_bv_tvtk_raw
-where "permute_bv_tvtk_raw p TVTKNil_raw = TVTKNil_raw"
-|     "permute_bv_tvtk_raw p (TVTKCons_raw v t l) = TVTKCons_raw (p \<bullet> v) t (permute_bv_tvtk_raw p l)"
+primrec permute_bv_vs_raw
+where "permute_bv_vs_raw p VsNil_raw = VsNil_raw"
+|     "permute_bv_vs_raw p (VsCons_raw v t l) = VsCons_raw (p \<bullet> v) t (permute_bv_vs_raw p l)"
+primrec permute_bv_cvs_raw
+where "permute_bv_cvs_raw p CvsNil_raw = CvsNil_raw"
+|     "permute_bv_cvs_raw p (CvsCons_raw v t l) = CvsCons_raw (p \<bullet> v) t (permute_bv_cvs_raw p l)"
+primrec permute_bv_tvs_raw
+where "permute_bv_tvs_raw p TvsNil_raw = TvsNil_raw"
+|     "permute_bv_tvs_raw p (TvsCons_raw v t l) = TvsCons_raw (p \<bullet> v) t (permute_bv_tvs_raw p l)"
 primrec permute_bv_raw
-where "permute_bv_raw p (K_raw c l1 l2 l3) =
-     K_raw c (permute_bv_tvtk_raw p l1) (permute_bv_tvck_raw p l2) (permute_bv_vt_raw p l3)"
+where "permute_bv_raw p (Kpat_raw c l1 l2 l3) =
+     Kpat_raw c (permute_bv_tvs_raw p l1) (permute_bv_cvs_raw p l2) (permute_bv_vs_raw p l3)"
 
-quotient_definition "permute_bv_vt :: perm \<Rightarrow> vt_lst \<Rightarrow> vt_lst"
-is "permute_bv_vt_raw"
-quotient_definition "permute_bv_tvck :: perm \<Rightarrow> tvck_lst \<Rightarrow> tvck_lst"
-is "permute_bv_tvck_raw"
-quotient_definition "permute_bv_tvtk :: perm \<Rightarrow> tvtk_lst \<Rightarrow> tvtk_lst"
-is "permute_bv_tvtk_raw"
+quotient_definition "permute_bv_vs :: perm \<Rightarrow> vars \<Rightarrow> vars"
+is "permute_bv_vs_raw"
+quotient_definition "permute_bv_cvs :: perm \<Rightarrow> cvars \<Rightarrow> cvars"
+is "permute_bv_cvs_raw"
+quotient_definition "permute_bv_tvs :: perm \<Rightarrow> tvars \<Rightarrow> tvars"
+is "permute_bv_tvs_raw"
 quotient_definition "permute_bv :: perm \<Rightarrow> pat \<Rightarrow> pat"
 is "permute_bv_raw"
 
 lemma rsp_pre:
- "alpha_tvtk_lst_raw d a \<Longrightarrow> alpha_tvtk_lst_raw (permute_bv_tvtk_raw x d) (permute_bv_tvtk_raw x a)"
- "alpha_tvck_lst_raw e b \<Longrightarrow> alpha_tvck_lst_raw (permute_bv_tvck_raw x e) (permute_bv_tvck_raw x b)"
- "alpha_vt_lst_raw f c \<Longrightarrow> alpha_vt_lst_raw (permute_bv_vt_raw x f) (permute_bv_vt_raw x c)"
+ "alpha_tvars_raw d a \<Longrightarrow> alpha_tvars_raw (permute_bv_tvs_raw x d) (permute_bv_tvs_raw x a)"
+ "alpha_cvars_raw e b \<Longrightarrow> alpha_cvars_raw (permute_bv_cvs_raw x e) (permute_bv_cvs_raw x b)"
+ "alpha_vars_raw f c \<Longrightarrow> alpha_vars_raw (permute_bv_vs_raw x f) (permute_bv_vs_raw x c)"
  apply (erule_tac [!] alpha_inducts)
  apply simp_all
  apply (rule_tac [!] alpha_intros)
@@ -135,9 +135,9 @@
 
 lemma [quot_respect]:
  "(op = ===> alpha_pat_raw ===> alpha_pat_raw) permute_bv_raw permute_bv_raw"
- "(op = ===> alpha_tvtk_lst_raw ===> alpha_tvtk_lst_raw) permute_bv_tvtk_raw permute_bv_tvtk_raw"
- "(op = ===> alpha_tvck_lst_raw ===> alpha_tvck_lst_raw) permute_bv_tvck_raw permute_bv_tvck_raw"
- "(op = ===> alpha_vt_lst_raw ===> alpha_vt_lst_raw) permute_bv_vt_raw permute_bv_vt_raw"
+ "(op = ===> alpha_tvars_raw ===> alpha_tvars_raw) permute_bv_tvs_raw permute_bv_tvs_raw"
+ "(op = ===> alpha_cvars_raw ===> alpha_cvars_raw) permute_bv_cvs_raw permute_bv_cvs_raw"
+ "(op = ===> alpha_vars_raw ===> alpha_vars_raw) permute_bv_vs_raw permute_bv_vs_raw"
  apply (simp_all add: rsp_pre)
  apply clarify
  apply (erule_tac alpha_inducts)
@@ -147,25 +147,25 @@
  done
 
 thm permute_bv_raw.simps[no_vars]
- permute_bv_vt_raw.simps[quot_lifted]
- permute_bv_tvck_raw.simps[quot_lifted]
- permute_bv_tvtk_raw.simps[quot_lifted]
+ permute_bv_vs_raw.simps[quot_lifted]
+ permute_bv_cvs_raw.simps[quot_lifted]
+ permute_bv_tvs_raw.simps[quot_lifted]
 
 lemma permute_bv_pre:
-  "permute_bv p (K c l1 l2 l3) =
-   K c (permute_bv_tvtk p l1) (permute_bv_tvck p l2) (permute_bv_vt p l3)"
+  "permute_bv p (Kpat c l1 l2 l3) =
+   Kpat c (permute_bv_tvs p l1) (permute_bv_cvs p l2) (permute_bv_vs p l3)"
   by (lifting permute_bv_raw.simps)
 
 lemmas permute_bv[simp] =
  permute_bv_pre
- permute_bv_vt_raw.simps[quot_lifted]
- permute_bv_tvck_raw.simps[quot_lifted]
- permute_bv_tvtk_raw.simps[quot_lifted]
+ permute_bv_vs_raw.simps[quot_lifted]
+ permute_bv_cvs_raw.simps[quot_lifted]
+ permute_bv_tvs_raw.simps[quot_lifted]
 
 lemma perm_bv1:
-  "p \<bullet> bv_tvck b = bv_tvck (permute_bv_tvck p b)"
-  "p \<bullet> bv_tvtk c = bv_tvtk (permute_bv_tvtk p c)"
-  "p \<bullet> bv_vt d = bv_vt (permute_bv_vt p d)"
+  "p \<bullet> bv_cvs b = bv_cvs (permute_bv_cvs p b)"
+  "p \<bullet> bv_tvs c = bv_tvs (permute_bv_tvs p c)"
+  "p \<bullet> bv_vs d = bv_vs (permute_bv_vs p d)"
   apply(induct b rule: inducts(12))
   apply(rule TrueI)
   apply(simp_all add:permute_bv eqvts)
@@ -187,14 +187,14 @@
   done
 
 lemma alpha_perm_bn1:
- " alpha_bv_tvtk tvtk_lst (permute_bv_tvtk q tvtk_lst)"
- "alpha_bv_tvck tvck_lst (permute_bv_tvck q tvck_lst)"
- "alpha_bv_vt vt_lst (permute_bv_vt q vt_lst)"
-  apply(induct tvtk_lst rule: inducts(11))
+ " alpha_bv_tvs tvars (permute_bv_tvs q tvars)"
+ "alpha_bv_cvs cvars (permute_bv_cvs q cvars)"
+ "alpha_bv_vs vars (permute_bv_vs q vars)"
+  apply(induct tvars rule: inducts(11))
   apply(simp_all add:permute_bv eqvts eq_iff)
-  apply(induct tvck_lst rule: inducts(12))
+  apply(induct cvars rule: inducts(12))
   apply(simp_all add:permute_bv eqvts eq_iff)
-  apply(induct vt_lst rule: inducts(10))
+  apply(induct vars rule: inducts(10))
   apply(simp_all add:permute_bv eqvts eq_iff)
   done
 
@@ -222,9 +222,9 @@
   done
 
 lemma permute_bv_zero1:
-  "permute_bv_tvck 0 b = b"
-  "permute_bv_tvtk 0 c = c"
-  "permute_bv_vt 0 d = d"
+  "permute_bv_cvs 0 b = b"
+  "permute_bv_tvs 0 c = c"
+  "permute_bv_vs 0 d = d"
   apply(induct b rule: inducts(12))
   apply(rule TrueI)
   apply(simp_all add:permute_bv eqvts)
@@ -243,7 +243,7 @@
   apply(simp_all add:permute_bv eqvts permute_bv_zero1)
   done
 
-lemma fv_alpha1: "fv_bv_tvtk x \<sharp>* pa \<Longrightarrow> alpha_bv_tvtk (pa \<bullet> x) x"
+lemma fv_alpha1: "fv_bv_tvs x \<sharp>* pa \<Longrightarrow> alpha_bv_tvs (pa \<bullet> x) x"
 apply (induct x rule: inducts(11))
 apply (tactic {* ALLGOALS (TRY o rtac @{thm TrueI}) *})
 apply (simp_all add: eq_iff fresh_star_union)
@@ -251,7 +251,7 @@
 apply (simp_all add: fv_supp)
 done
 
-lemma fv_alpha2: "fv_bv_tvck x \<sharp>* pa \<Longrightarrow> alpha_bv_tvck (pa \<bullet> x) x"
+lemma fv_alpha2: "fv_bv_cvs x \<sharp>* pa \<Longrightarrow> alpha_bv_cvs (pa \<bullet> x) x"
 apply (induct x rule: inducts(12))
 apply (tactic {* ALLGOALS (TRY o rtac @{thm TrueI}) *})
 apply (simp_all add: eq_iff fresh_star_union)
@@ -259,7 +259,7 @@
 apply (simp_all add: fv_supp)
 done
 
-lemma fv_alpha3: "fv_bv_vt x \<sharp>* pa \<Longrightarrow> alpha_bv_vt (pa \<bullet> x) x"
+lemma fv_alpha3: "fv_bv_vs x \<sharp>* pa \<Longrightarrow> alpha_bv_vs (pa \<bullet> x) x"
 apply (induct x rule: inducts(10))
 apply (tactic {* ALLGOALS (TRY o rtac @{thm TrueI}) *})
 apply (simp_all add: eq_iff fresh_star_union)
@@ -275,19 +275,19 @@
 apply (simp add: eqvts)
 done
 
-lemma fin1: "finite (fv_bv_tvtk x)"
+lemma fin1: "finite (fv_bv_tvs x)"
 apply (induct x rule: inducts(11))
 apply (tactic {* ALLGOALS (TRY o rtac @{thm TrueI}) *})
 apply (simp_all add: fv_supp finite_supp)
 done
 
-lemma fin2: "finite (fv_bv_tvck x)"
+lemma fin2: "finite (fv_bv_cvs x)"
 apply (induct x rule: inducts(12))
 apply (tactic {* ALLGOALS (TRY o rtac @{thm TrueI}) *})
 apply (simp_all add: fv_supp finite_supp)
 done
 
-lemma fin3: "finite (fv_bv_vt x)"
+lemma fin3: "finite (fv_bv_vs x)"
 apply (induct x rule: inducts(10))
 apply (tactic {* ALLGOALS (TRY o rtac @{thm TrueI}) *})
 apply (simp_all add: fv_supp finite_supp)
@@ -299,19 +299,19 @@
 apply (simp add: fin1 fin2 fin3)
 done
 
-lemma finb1: "finite (set (bv_tvtk x))"
+lemma finb1: "finite (set (bv_tvs x))"
 apply (induct x rule: inducts(11))
 apply (tactic {* ALLGOALS (TRY o rtac @{thm TrueI}) *})
 apply (simp_all add: fv_supp finite_supp)
 done
 
-lemma finb2: "finite (set (bv_tvck x))"
+lemma finb2: "finite (set (bv_cvs x))"
 apply (induct x rule: inducts(12))
 apply (tactic {* ALLGOALS (TRY o rtac @{thm TrueI}) *})
 apply (simp_all add: fv_supp finite_supp)
 done
 
-lemma finb3: "finite (set (bv_vt x))"
+lemma finb3: "finite (set (bv_vs x))"
 apply (induct x rule: inducts(10))
 apply (tactic {* ALLGOALS (TRY o rtac @{thm TrueI}) *})
 apply (simp_all add: fv_supp finite_supp)
@@ -334,8 +334,8 @@
   and a08: "\<And>tvar tkind ty b. \<lbrakk>\<And>c. P1 c tkind; \<And>c. P3 c ty; atom tvar \<sharp> b\<rbrakk>
     \<Longrightarrow> P3 b (TAll tvar tkind ty)"
   and a09: "\<And>ty1 ty2 ty3 b. \<lbrakk>\<And>c. P3 c ty1; \<And>c. P3 c ty2; \<And>c. P3 c ty3\<rbrakk> \<Longrightarrow> P3 b (TEq ty1 ty2 ty3)"
-  and a10: "\<And>b. P4 b TsNil"
-  and a11: "\<And>ty ty_lst b. \<lbrakk>\<And>c. P3 c ty; \<And>c. P4 c ty_lst\<rbrakk> \<Longrightarrow> P4 b (TsCons ty ty_lst)"
+  and a10: "\<And>b. P4 b TvsNil"
+  and a11: "\<And>ty ty_lst b. \<lbrakk>\<And>c. P3 c ty; \<And>c. P4 c ty_lst\<rbrakk> \<Longrightarrow> P4 b (TvsCons ty ty_lst)"
   and a12: "\<And>string b. P5 b (CC string)"
   and a13: "\<And>co1 co2 b. \<lbrakk>\<And>c. P5 c co1; \<And>c. P5 c co2\<rbrakk> \<Longrightarrow> P5 b (CApp co1 co2)"
   and a14: "\<And>string co_lst b. \<lbrakk>\<And>c. P6 c co_lst\<rbrakk> \<Longrightarrow> P5 b (CFun string co_lst)"
@@ -368,16 +368,16 @@
   and a37: "\<And>b. P8 b ANil"
   and a38: "\<And>pat trm assoc_lst b. \<lbrakk>\<And>c. P9 c pat; \<And>c. P7 c trm; \<And>c. P8 c assoc_lst; set (bv (pat)) \<sharp>* b\<rbrakk>
     \<Longrightarrow> P8 b (ACons pat trm assoc_lst)"
-  and a39: "\<And>string tvtk_lst tvck_lst vt_lst b. \<lbrakk>\<And>c. P11 c tvtk_lst; \<And>c. P12 c tvck_lst; \<And>c. P10 c vt_lst\<rbrakk>
-    \<Longrightarrow> P9 b (K string tvtk_lst tvck_lst vt_lst)"
-  and a40: "\<And>b. P10 b VTNil"
-  and a41: "\<And>var ty vt_lst b. \<lbrakk>\<And>c. P3 c ty; \<And>c. P10 c vt_lst\<rbrakk> \<Longrightarrow> P10 b (VTCons var ty vt_lst)"
-  and a42: "\<And>b. P11 b TVTKNil"
-  and a43: "\<And>tvar tkind tvtk_lst b. \<lbrakk>\<And>c. P1 c tkind; \<And>c. P11 c tvtk_lst\<rbrakk>
-    \<Longrightarrow> P11 b (TVTKCons tvar tkind tvtk_lst)"
-  and a44: "\<And>b. P12 b TVCKNil"
-  and a45: "\<And>tvar ckind tvck_lst b. \<lbrakk>\<And>c. P2 c ckind; \<And>c. P12 c tvck_lst\<rbrakk>
-    \<Longrightarrow> P12 b (TVCKCons tvar ckind tvck_lst)"
+  and a39: "\<And>string tvars cvars vars b. \<lbrakk>\<And>c. P11 c tvars; \<And>c. P12 c cvars; \<And>c. P10 c vars\<rbrakk>
+    \<Longrightarrow> P9 b (K string tvars cvars vars)"
+  and a40: "\<And>b. P10 b VsNil"
+  and a41: "\<And>var ty vars b. \<lbrakk>\<And>c. P3 c ty; \<And>c. P10 c vars\<rbrakk> \<Longrightarrow> P10 b (VsCons var ty vars)"
+  and a42: "\<And>b. P11 b TvsNil"
+  and a43: "\<And>tvar tkind tvars b. \<lbrakk>\<And>c. P1 c tkind; \<And>c. P11 c tvars\<rbrakk>
+    \<Longrightarrow> P11 b (TvsCons tvar tkind tvars)"
+  and a44: "\<And>b. P12 b CvsNil"
+  and a45: "\<And>tvar ckind cvars b. \<lbrakk>\<And>c. P2 c ckind; \<And>c. P12 c cvars\<rbrakk>
+    \<Longrightarrow> P12 b (CvsCons tvar ckind cvars)"
   shows "P1 (a :: 'a :: pt) tkind \<and>
          P2 (b :: 'b :: pt) ckind \<and>
          P3 (c :: 'c :: {pt,fs}) ty \<and>
@@ -387,12 +387,12 @@
          P7 (g :: 'g :: {pt,fs}) trm \<and>
          P8 (h :: 'h :: {pt,fs}) assoc_lst \<and>
          P9 (i :: 'i :: pt) pat \<and>
-         P10 (j :: 'j :: pt) vt_lst \<and>
-         P11 (k :: 'k :: pt) tvtk_lst \<and>
-         P12 (l :: 'l :: pt) tvck_lst"
+         P10 (j :: 'j :: pt) vars \<and>
+         P11 (k :: 'k :: pt) tvars \<and>
+         P12 (l :: 'l :: pt) cvars"
 proof -
-  have a1: "(\<forall>p a. P1 a (p \<bullet> tkind))" and "(\<forall>p b. P2 b (p \<bullet> ckind))" and "(\<forall>p c. P3 c (p \<bullet> ty))" and "(\<forall>p d. P4 d (p \<bullet> ty_lst))" and "(\<forall>p e. P5 e (p \<bullet> co))" and " (\<forall>p f. P6 f (p \<bullet> co_lst))" and "(\<forall>p g. P7 g (p \<bullet> trm))" and "(\<forall>p h. P8 h (p \<bullet> assoc_lst))" and a1:"(\<forall>p q i. P9 i (permute_bv p (q \<bullet> pat)))" and a2:"(\<forall>p q j. P10 j (permute_bv_vt q (p \<bullet> vt_lst)))" and a3:"(\<forall>p q k. P11 k ( permute_bv_tvtk q (p \<bullet> tvtk_lst)))" and a4:"(\<forall>p q l. P12 l (permute_bv_tvck q (p \<bullet> tvck_lst)))"
-    apply (induct rule: tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vt_lst_tvtk_lst_tvck_lst.inducts)
+  have a1: "(\<forall>p a. P1 a (p \<bullet> tkind))" and "(\<forall>p b. P2 b (p \<bullet> ckind))" and "(\<forall>p c. P3 c (p \<bullet> ty))" and "(\<forall>p d. P4 d (p \<bullet> ty_lst))" and "(\<forall>p e. P5 e (p \<bullet> co))" and " (\<forall>p f. P6 f (p \<bullet> co_lst))" and "(\<forall>p g. P7 g (p \<bullet> trm))" and "(\<forall>p h. P8 h (p \<bullet> assoc_lst))" and a1:"(\<forall>p q i. P9 i (permute_bv p (q \<bullet> pat)))" and a2:"(\<forall>p q j. P10 j (permute_bv_vs q (p \<bullet> vars)))" and a3:"(\<forall>p q k. P11 k ( permute_bv_tvs q (p \<bullet> tvars)))" and a4:"(\<forall>p q l. P12 l (permute_bv_cvs q (p \<bullet> cvars)))"
+    apply (induct rule: tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.inducts)
     apply (tactic {* ALLGOALS (REPEAT o rtac allI) *})
     apply (tactic {* ALLGOALS (TRY o SOLVED' (simp_tac @{simpset} THEN_ALL_NEW resolve_tac @{thms assms} THEN_ALL_NEW asm_full_simp_tac @{simpset})) *})
 
@@ -663,7 +663,7 @@
     apply (simp add: fresh_star_def fresh_def supp_abs eqvts)
     done
   then have b: "P1 a (0 \<bullet> tkind)" and "P2 b (0 \<bullet> ckind)" "P3 c (0 \<bullet> ty)" and "P4 d (0 \<bullet> ty_lst)" and "P5 e (0 \<bullet> co)" and "P6 f (0 \<bullet> co_lst)" and "P7 g (0 \<bullet> trm)" and "P8 h (0 \<bullet> assoc_lst)" by (blast+)
-  moreover have "P9  i (permute_bv 0 (0 \<bullet> pat))" and "P10 j (permute_bv_vt 0 (0 \<bullet> vt_lst))" and "P11 k (permute_bv_tvtk 0 (0 \<bullet> tvtk_lst))" and "P12 l (permute_bv_tvck 0 (0 \<bullet> tvck_lst))" using a1 a2 a3 a4 by (blast+)
+  moreover have "P9  i (permute_bv 0 (0 \<bullet> pat))" and "P10 j (permute_bv_vs 0 (0 \<bullet> vars))" and "P11 k (permute_bv_tvs 0 (0 \<bullet> tvars))" and "P12 l (permute_bv_cvs 0 (0 \<bullet> cvars))" using a1 a2 a3 a4 by (blast+)
   ultimately show ?thesis by (simp_all add: permute_bv_zero1 permute_bv_zero2)
 qed