--- a/Nominal/Ex/LetSimple1.thy	Sat Dec 17 17:03:01 2011 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,111 +0,0 @@
-theory LetSimple1
-imports "../Nominal2" 
-begin
-
-atom_decl name
-
-nominal_datatype trm =
-  Var "name"
-| App "trm" "trm"
-| Let x::"name" "trm" t::"trm"   binds x in t
-
-print_theorems
-
-thm trm.fv_defs
-thm trm.eq_iff 
-thm trm.bn_defs
-thm trm.bn_inducts
-thm trm.perm_simps
-thm trm.induct
-thm trm.inducts
-thm trm.distinct
-thm trm.supp
-thm trm.fresh
-thm trm.exhaust
-thm trm.strong_exhaust
-thm trm.perm_bn_simps
-
-nominal_primrec
-    height_trm :: "trm \<Rightarrow> nat"
-where
-  "height_trm (Var x) = 1"
-| "height_trm (App l r) = max (height_trm l) (height_trm r)"
-| "height_trm (Let x t s) = max (height_trm t) (height_trm s)"
-  apply (simp only: eqvt_def height_trm_graph_def)
-  apply (rule, perm_simp, rule, rule TrueI)
-  apply (case_tac x rule: trm.exhaust(1))
-  apply (auto)[3]
-  apply(simp_all)[5]
-  apply (subgoal_tac "height_trm_sumC t = height_trm_sumC ta")
-  apply (subgoal_tac "height_trm_sumC s = height_trm_sumC sa")
-  apply simp
-  apply(simp)
-  apply(erule conjE)
-  apply(erule_tac c="()" in Abs_lst1_fcb2)
-  apply(simp_all add: fresh_star_def pure_fresh)[2]
-  apply(simp_all add: eqvt_at_def)[2]
-  apply(simp)
-  done
-
-termination
-  by lexicographic_order
-
-
-nominal_primrec (invariant "\<lambda>x (y::atom set). finite y")
-  frees_set :: "trm \<Rightarrow> atom set"
-where
-  "frees_set (Var x) = {atom x}"
-| "frees_set (App t1 t2) = frees_set t1 \<union> frees_set t2"
-| "frees_set (Let x t s) = (frees_set s) - {atom x} \<union> (frees_set t)"
-  apply(simp add: eqvt_def frees_set_graph_def)
-  apply(rule, perm_simp, rule)
-  apply(erule frees_set_graph.induct)
-  apply(auto)[3]
-  apply(rule_tac y="x" in trm.exhaust)
-  apply(auto)[3]
-  apply(simp_all)[5]
-  apply(simp)
-  apply(erule conjE)
-  apply(subgoal_tac "frees_set_sumC s - {atom x} = frees_set_sumC sa - {atom xa}")
-  apply(simp)
-  apply(erule_tac c="()" in Abs_lst1_fcb2)
-  apply(simp add: fresh_minus_atom_set)
-  apply(simp add: fresh_star_def fresh_Unit)
-  apply(simp add: Diff_eqvt eqvt_at_def, perm_simp, rule refl)
-  apply(simp add: Diff_eqvt eqvt_at_def, perm_simp, rule refl)
-  done
-
-termination
-  by lexicographic_order
-
-
-nominal_primrec
-  subst :: "trm \<Rightarrow> name \<Rightarrow> trm \<Rightarrow> trm"  ("_ [_ ::= _]" [90, 90, 90] 90)
-where
-  "(Var x)[y ::= s] = (if x = y then s else (Var x))"
-| "(App t1 t2)[y ::= s] = App (t1[y ::= s]) (t2[y ::= s])"
-| "atom x \<sharp> (y, s) \<Longrightarrow> (Let x t t')[y ::= s] = Let x (t[y ::= s]) (t'[y ::= s])"
-  apply(simp add: eqvt_def subst_graph_def)
-  apply (rule, perm_simp, rule)
-  apply(rule TrueI)
-  apply(auto)[1]
-  apply(rule_tac y="a" and c="(aa, b)" in trm.strong_exhaust)
-  apply(blast)+
-  apply(simp_all add: fresh_star_def fresh_Pair_elim)[1]
-  apply(blast)
-  apply(simp_all)[5]
-  apply(simp (no_asm_use))
-  apply(simp)
-  apply(erule conjE)+
-  apply (erule_tac c="(ya,sa)" in Abs_lst1_fcb2)
-  apply(simp add: Abs_fresh_iff)
-  apply(simp add: fresh_star_def fresh_Pair)
-  apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
-  apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
-done
-
-termination
-  by lexicographic_order
-
-
-end
\ No newline at end of file