--- a/Nominal/Rsp.thy	Mon Mar 22 14:07:35 2010 +0100
+++ b/Nominal/Rsp.thy	Mon Mar 22 15:27:01 2010 +0100
@@ -259,5 +259,47 @@
 end
 *}
 
+lemma equivp_rspl:
+  "equivp r \<Longrightarrow> r a b \<Longrightarrow> r a c = r b c"
+  unfolding equivp_reflp_symp_transp symp_def transp_def 
+  by blast
+
+lemma equivp_rspr:
+  "equivp r \<Longrightarrow> r a b \<Longrightarrow> r c a = r c b"
+  unfolding equivp_reflp_symp_transp symp_def transp_def 
+  by blast
+
+ML {*
+fun prove_alpha_bn_rsp alphas inducts inj_dis equivps ctxt (alpha_bn, n) =
+let
+  val alpha = nth alphas n;
+  val ty = domain_type (fastype_of alpha);
+  val names = Datatype_Prop.make_tnames [ty, ty];
+  val [l, r] = map (fn x => (Free (x, ty))) names;
+  val g1 =
+    Logic.mk_implies (HOLogic.mk_Trueprop (alpha $ l $ r),
+      HOLogic.mk_Trueprop (HOLogic.mk_all ("a", ty,
+        HOLogic.mk_eq (alpha_bn $ l $ Bound 0, alpha_bn $ r $ Bound 0))))
+  val g2 =
+    Logic.mk_implies (HOLogic.mk_Trueprop (alpha $ l $ r),
+      HOLogic.mk_Trueprop (HOLogic.mk_all ("a", ty,
+        HOLogic.mk_eq (alpha_bn $ Bound 0 $ l, alpha_bn $ Bound 0 $ r))))
+  fun tac {context, ...} = (
+    etac (nth inducts n) THEN_ALL_NEW
+    (TRY o rtac @{thm TrueI}) THEN_ALL_NEW rtac allI THEN_ALL_NEW
+    InductTacs.case_tac context "a" THEN_ALL_NEW split_conjs THEN_ALL_NEW
+    asm_full_simp_tac (HOL_ss addsimps inj_dis) THEN_ALL_NEW
+    REPEAT_ALL_NEW (rtac @{thm arg_cong2[of _ _ _ _ "op \<and>"]}) THEN_ALL_NEW
+    TRY o eresolve_tac (map (fn x => @{thm equivp_rspl} OF [x]) equivps) THEN_ALL_NEW
+    TRY o eresolve_tac (map (fn x => @{thm equivp_rspr} OF [x]) equivps) THEN_ALL_NEW
+    TRY o rtac refl
+  ) 1;
+  val t1 = Goal.prove ctxt names [] g1 tac;
+  val t2 = Goal.prove ctxt names [] g2 tac;
+in
+  [t1, t2]
+end
+*}
+
 
 end