--- a/Nominal/Ex/SingleLet.thy	Sat Sep 25 02:53:39 2010 +0200
+++ b/Nominal/Ex/SingleLet.thy	Sat Sep 25 08:28:45 2010 -0400
@@ -36,131 +36,7 @@
 thm single_let.fsupp
 thm single_let.supp
 
-lemma test2:
-  assumes "fv_trm t = supp t" 
-  shows "\<forall>p. fv_trm (p \<bullet> t) = supp (p \<bullet> t)"
-apply(rule allI)
-apply(rule_tac p="-p" in permute_boolE)
-apply(perm_simp add: single_let.fv_bn_eqvt permute_minus_cancel)
-apply(rule assms)
-done
 
-lemma supp_fv:
-  "fv_trm x = supp x" 
-  "fv_assg xa = supp xa"
-  "fv_bn xa = supp_rel alpha_bn xa"
-apply(induct rule: single_let.inducts)
--- " 0A "
-apply(simp only: single_let.fv_defs supp_Pair[symmetric])
-apply(simp (no_asm) only: supp_def)
-apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt)
-apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff)
--- " 0B"
-apply(simp only: single_let.fv_defs supp_Pair[symmetric])
-apply(simp (no_asm) only: supp_def)
-apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt)
-apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff)
-apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject)
---" 1 "
-apply(simp only: single_let.fv_defs supp_Pair[symmetric])
-apply(tactic {* EqSubst.eqsubst_tac @{context} [1] @{thms supp_abs(3)[symmetric]} 1 *})
-apply(simp (no_asm) only: supp_def)
-apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt)
-apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff)
-apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject)
-apply(drule test2)
-apply(simp only:)
--- " 2 "
-apply(simp only: single_let.fv_defs supp_Pair[symmetric])
-apply(subst supp_abs(3)[symmetric])
-apply(simp (no_asm) only: supp_def supp_rel_def)
-apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt)
-apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff)
-apply(simp only: de_Morgan_conj Collect_disj_eq finite_Un)
-apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject)
-apply(drule test2)
-apply(simp only:)
--- " 3 "
-apply(simp only: single_let.fv_defs supp_Pair[symmetric])
-apply(subst supp_abs(1)[symmetric])
-apply(simp (no_asm) only: supp_def supp_rel_def)
-apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt)
-apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff)
-apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject)
-apply(drule test2)+
-apply(simp only: supp_Pair Un_assoc conj_assoc)
--- " Bar "
-apply(simp only: single_let.fv_defs supp_Pair[symmetric])
-apply(subst supp_abs(3)[symmetric])
-apply(simp (no_asm) only: supp_def)
-apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt)
-apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff)
-apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject)
-apply(drule test2)+
-apply(simp only: supp_Pair Un_assoc conj_assoc)
--- " Baz "
-apply(simp only: single_let.fv_defs supp_Pair[symmetric])
-apply(subst supp_abs(1)[symmetric])
-apply(subst supp_abs(1)[symmetric])
-apply(simp (no_asm) only: supp_def)
-apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt)
-apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff)
-apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject)
-apply(simp only: de_Morgan_conj Collect_disj_eq finite_Un)
-apply(drule test2)+
-apply(simp only: supp_Pair Un_assoc conj_assoc)
--- "last"
-apply(simp only: single_let.fv_defs supp_Pair[symmetric])
-apply(tactic {* EqSubst.eqsubst_tac @{context} [1] @{thms supp_abs(3)[symmetric]} 1 *})
-apply(simp (no_asm) only: supp_def supp_rel_def)
-apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt)
-apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff)
-apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject)
-apply(simp only: de_Morgan_conj Collect_disj_eq finite_Un)
-apply(drule test2)+
-apply(simp only: supp_Pair Un_assoc conj_assoc)
--- "other case"
-apply(simp only: single_let.fv_defs supp_Pair[symmetric])
-apply(simp only: supp_abs(3)[symmetric])
-apply(simp (no_asm) only: supp_def supp_rel_def)
-apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt)
-apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff)
-apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject)
-apply(simp only: de_Morgan_conj Collect_disj_eq finite_Un)?
-apply(drule test2)+
-apply(simp only: supp_Pair Un_assoc conj_assoc)
-done
-
-
-
-
-
-text {* *}
-
-(*
-consts perm_bn_trm :: "perm \<Rightarrow> trm \<Rightarrow> trm"
-consts perm_bn_assg :: "perm \<Rightarrow> assg \<Rightarrow> assg"
-
-lemma y:
-  "perm_bn_trm p (Var x) = (Var x)"
-  "perm_bn_trm p (App t1 t2) = (App t1 t2)"
-  "perm_bn_trm p ("
-
-
-
-typ trm
-typ assg
-
-thm trm_assg.fv
-thm trm_assg.supp
-thm trm_assg.eq_iff
-thm trm_assg.bn
-thm trm_assg.perm
-thm trm_assg.induct
-thm trm_assg.inducts
-thm trm_assg.distinct
-ML {* Sign.of_sort @{theory} (@{typ trm}, @{sort fs}) *}
-*)