--- a/LFex.thy	Sun Dec 06 23:32:27 2009 +0100
+++ b/LFex.thy	Sun Dec 06 23:35:02 2009 +0100
@@ -287,16 +287,16 @@
 using a0 a1 a2 a3 a4 a5 a6 a7 a8
 *)
 
-lemma "\<lbrakk>P1 TYP;
-  \<And>ty name kind. \<lbrakk>P2 ty; P1 kind\<rbrakk> \<Longrightarrow> P1 (KPI ty name kind);
-  \<And>id. P2 (TCONST id);
-  \<And>ty trm. \<lbrakk>P2 ty; P3 trm\<rbrakk> \<Longrightarrow> P2 (TAPP ty trm);
-  \<And>ty1 name ty2. \<lbrakk>P2 ty1; P2 ty2\<rbrakk> \<Longrightarrow> P2 (TPI ty1 name ty2);
-  \<And>id. P3 (CONS id); \<And>name. P3 (VAR name);
-  \<And>trm1 trm2. \<lbrakk>P3 trm1; P3 trm2\<rbrakk> \<Longrightarrow> P3 (APP trm1 trm2);
-  \<And>ty name trm. \<lbrakk>P2 ty; P3 trm\<rbrakk> \<Longrightarrow> P3 (LAM ty name trm)\<rbrakk>
-  \<Longrightarrow> P1 mkind \<and> P2 mty \<and> P3 mtrm"
-apply(tactic {* lift_tac @{context} @{thm kind_ty_trm.induct} 1 *})
+lemma "\<lbrakk>P TYP;
+  \<And>ty name kind. \<lbrakk>Q ty; P kind\<rbrakk> \<Longrightarrow> P (KPI ty name kind);
+  \<And>id. Q (TCONST id);
+  \<And>ty trm. \<lbrakk>Q ty; R trm\<rbrakk> \<Longrightarrow> Q (TAPP ty trm);
+  \<And>ty1 name ty2. \<lbrakk>Q ty1; Q ty2\<rbrakk> \<Longrightarrow> Q (TPI ty1 name ty2);
+  \<And>id. R (CONS id); \<And>name. R (VAR name);
+  \<And>trm1 trm2. \<lbrakk>R trm1; R trm2\<rbrakk> \<Longrightarrow> R (APP trm1 trm2);
+  \<And>ty name trm. \<lbrakk>Q ty; R trm\<rbrakk> \<Longrightarrow> R (LAM ty name trm)\<rbrakk>
+  \<Longrightarrow> P mkind \<and> Q mty \<and> R mtrm"
+apply(tactic {* lift_tac @{context} @{thm kind_ty_trm.induct} @{thms alpha_equivps} 1 *})
 done
 
 print_quotients