--- a/Nominal/LamEx.thy	Tue Mar 23 08:46:44 2010 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,91 +0,0 @@
-theory LamEx
-imports "Parser" "../Attic/Prove"
-begin
-
-atom_decl name
-
-nominal_datatype lm =
-  Vr "name"
-| Ap "lm" "lm"
-| Lm x::"name" l::"lm"  bind x in l
-
-lemmas supp_fn' = lm.fv[simplified lm.supp]
-
-lemma
-  fixes c::"'a::fs"
-  assumes a1: "\<And>name c. P c (Vr name)"
-  and     a2: "\<And>lm1 lm2 c. \<lbrakk>\<And>d. P d lm1; \<And>d. P d lm2\<rbrakk> \<Longrightarrow> P c (Ap lm1 lm2)"
-  and     a3: "\<And>name lm c. \<lbrakk>atom name \<sharp> c; \<And>d. P d lm\<rbrakk> \<Longrightarrow> P c (Lm name lm)"
-  shows "P c lm"
-proof -
-  have "\<And>p. P c (p \<bullet> lm)"
-    apply(induct lm arbitrary: c rule: lm.induct)
-    apply(simp only: lm.perm)
-    apply(rule a1)
-    apply(simp only: lm.perm)
-    apply(rule a2)
-    apply(blast)[1]
-    apply(assumption)
-    apply(subgoal_tac "\<exists>new::name. (atom new) \<sharp> (c, Lm (p \<bullet> name) (p \<bullet> lm))")
-    defer
-    apply(simp add: fresh_def)
-    apply(rule_tac X="supp (c, Lm (p \<bullet> name) (p \<bullet> lm))" in obtain_at_base)
-    apply(simp add: supp_Pair finite_supp)
-    apply(blast)
-    apply(erule exE)
-    apply(rule_tac t="p \<bullet> Lm name lm" and 
-                   s="(((p \<bullet> name) \<leftrightarrow> new) + p) \<bullet> Lm name lm" in subst)
-    apply(simp del: lm.perm)
-    apply(subst lm.perm)
-    apply(subst (2) lm.perm)
-    apply(rule flip_fresh_fresh)
-    apply(simp add: fresh_def)
-    apply(simp only: supp_fn')
-    apply(simp)
-    apply(simp add: fresh_Pair)
-    apply(simp)
-    apply(rule a3)
-    apply(simp add: fresh_Pair)
-    apply(drule_tac x="((p \<bullet> name) \<leftrightarrow> new) + p" in meta_spec)
-    apply(simp)
-    done
-  then have "P c (0 \<bullet> lm)" by blast
-  then show "P c lm" by simp
-qed
-
-
-lemma
-  fixes c::"'a::fs"
-  assumes a1: "\<And>name c. P c (Vr name)"
-  and     a2: "\<And>lm1 lm2 c. \<lbrakk>\<And>d. P d lm1; \<And>d. P d lm2\<rbrakk> \<Longrightarrow> P c (Ap lm1 lm2)"
-  and     a3: "\<And>name lm c. \<lbrakk>atom name \<sharp> c; \<And>d. P d lm\<rbrakk> \<Longrightarrow> P c (Lm name lm)"
-  shows "P c lm"
-proof -
-  have "\<And>p. P c (p \<bullet> lm)"
-    apply(induct lm arbitrary: c rule: lm.induct)
-    apply(simp only: lm.perm)
-    apply(rule a1)
-    apply(simp only: lm.perm)
-    apply(rule a2)
-    apply(blast)[1]
-    apply(assumption)
-    thm at_set_avoiding
-    apply(subgoal_tac "\<exists>q. (q \<bullet> {p \<bullet> atom name}) \<sharp>* c \<and> supp (p \<bullet> Lm name lm) \<sharp>* q")
-    apply(erule exE)
-    apply(rule_tac t="p \<bullet> Lm name lm" and 
-                   s="q \<bullet> p \<bullet> Lm name lm" in subst)
-    defer
-    apply(simp add: lm.perm)
-    apply(rule a3)
-    apply(simp add: eqvts fresh_star_def)
-    apply(drule_tac x="q + p" in meta_spec)
-    apply(simp)
-    sorry
-  then have "P c (0 \<bullet> lm)" by blast
-  then show "P c lm" by simp
-qed
-
-end
-
-
-