--- a/Nominal/Ex/LetRec2.thy	Sat Dec 17 17:03:01 2011 +0000
+++ b/Nominal/Ex/LetRec2.thy	Sat Dec 17 17:08:47 2011 +0000
@@ -5,82 +5,28 @@
 atom_decl name
 
 nominal_datatype trm =
-  Var "name"
-| App "trm" "trm"
-| Lam x::"name" t::"trm"  binds x in t
-| Let as::"assn" t::"trm"   binds "bn as" in t
-| Let_rec as::"assn" t::"trm"   binds "bn as" in as t
-and assn =
-  ANil
-| ACons "name" "trm" "assn"
+  Vr "name"
+| Ap "trm" "trm"
+| Lm x::"name" t::"trm"  binds (set) x in t
+| Lt a::"lts" t::"trm"   binds "bn a" in a t
+and lts =
+  Lnil
+| Lcons "name" "trm" "lts"
 binder
   bn
 where
-  "bn (ANil) = []"
-| "bn (ACons x t as) = (atom x) # (bn as)"
-
-thm trm_assn.eq_iff
-thm trm_assn.supp
-
-thm trm_assn.fv_defs
-thm trm_assn.eq_iff
-thm trm_assn.bn_defs
-thm trm_assn.perm_simps
-thm trm_assn.induct
-thm trm_assn.distinct
-
-
-
-section {* Tests *}
+  "bn Lnil = []"
+| "bn (Lcons x t l) = (atom x) # (bn l)"
 
 
-(* why is this not in HOL simpset? *)
-(*
-lemma set_sub: "{a, b} - {b} = {a} - {b}"
-by auto
-
-lemma lets_bla:
-  "x \<noteq> z \<Longrightarrow> y \<noteq> z \<Longrightarrow> x \<noteq> y \<Longrightarrow>(Lt (Lcons x (Vr y) Lnil) (Vr x)) \<noteq> (Lt (Lcons x (Vr z) Lnil) (Vr x))"
-  apply (auto simp add: trm_lts.eq_iff alphas set_sub supp_at_base)
-  done
-
-lemma lets_ok:
-  "(Lt (Lcons x (Vr x) Lnil) (Vr x)) = (Lt (Lcons y (Vr y) Lnil) (Vr y))"
-  apply (simp add: trm_lts.eq_iff)
-  apply (rule_tac x="(x \<leftrightarrow> y)" in exI)
-  apply (simp_all add: alphas fresh_star_def eqvts supp_at_base)
-  done
-
-lemma lets_ok3:
-  "x \<noteq> y \<Longrightarrow>
-   (Lt (Lcons x (Ap (Vr y) (Vr x)) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
-   (Lt (Lcons y (Ap (Vr x) (Vr y)) (Lcons x (Vr x) Lnil)) (Ap (Vr x) (Vr y)))"
-  apply (simp add: alphas trm_lts.eq_iff)
-  done
+thm trm_lts.fv_defs
+thm trm_lts.eq_iff
+thm trm_lts.bn_defs
+thm trm_lts.perm_simps
+thm trm_lts.induct
+thm trm_lts.distinct
 
 
-lemma lets_not_ok1:
-  "x \<noteq> y \<Longrightarrow>
-   (Lt (Lcons x (Vr x) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
-   (Lt (Lcons y (Vr x) (Lcons x (Vr y) Lnil)) (Ap (Vr x) (Vr y)))"
-  apply (simp add: alphas trm_lts.eq_iff)
-  done
-
-lemma lets_nok:
-  "x \<noteq> y \<Longrightarrow> x \<noteq> z \<Longrightarrow> z \<noteq> y \<Longrightarrow>
-   (Lt (Lcons x (Ap (Vr z) (Vr z)) (Lcons y (Vr z) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
-   (Lt (Lcons y (Vr z) (Lcons x (Ap (Vr z) (Vr z)) Lnil)) (Ap (Vr x) (Vr y)))"
-  apply (simp add: alphas trm_lts.eq_iff fresh_star_def)
-  done
-
-lemma lets_ok4:
-  "(Lt (Lcons x (Ap (Vr y) (Vr x)) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) =
-   (Lt (Lcons y (Ap (Vr x) (Vr y)) (Lcons x (Vr x) Lnil)) (Ap (Vr y) (Vr x)))"
-  apply (simp add: alphas trm_lts.eq_iff supp_at_base)
-  apply (rule_tac x="(x \<leftrightarrow> y)" in exI)
-  apply (simp add: atom_eqvt fresh_star_def)
-  done
-*)
 end