# HG changeset patch
# User Christian Urban <urbanc@in.tum.de>
# Date 1285417725 14400
# Node ID b4ea19604b0ba59e2845238685cd6e9bbc73148f
# Parent  6bab47906dbea2ccd5a5dddd70d57796b95b8a4d
cleaned up two examples

diff -r 6bab47906dbe -r b4ea19604b0b Nominal/Ex/SingleLet.thy
--- 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}) *}
-*)
 
 
 
diff -r 6bab47906dbe -r b4ea19604b0b Nominal/Ex/TypeSchemes.thy
--- a/Nominal/Ex/TypeSchemes.thy	Sat Sep 25 02:53:39 2010 +0200
+++ b/Nominal/Ex/TypeSchemes.thy	Sat Sep 25 08:28:45 2010 -0400
@@ -6,7 +6,7 @@
 
 atom_decl name
 
-declare [[STEPS = 100]]
+(* defined as a single nominal datatype *)
 
 nominal_datatype ty =
   Var "name"
@@ -26,6 +26,8 @@
 thm ty_tys.supports
 thm ty_tys.fsupp
 
+(* defined as two separate nominal datatypes *)
+
 nominal_datatype ty2 =
   Var2 "name"
 | Fun2 "ty2" "ty2"
@@ -50,8 +52,6 @@
 text {* *}
 
 (*
-ML {* Sign.of_sort @{theory} (@{typ ty}, @{sort fs}) *}
-
 lemma strong_induct:
   assumes a1: "\<And>name b. P b (Var name)"
   and     a2: "\<And>t1 t2 b. \<lbrakk>\<And>c. P c t1; \<And>c. P c t2\<rbrakk> \<Longrightarrow> P b (Fun t1 t2)"
@@ -74,7 +74,7 @@
                    s="pa \<bullet> (p \<bullet> All fset ty)" in subst)
     apply (rule supp_perm_eq)
     apply assumption
-    apply (simp only: ty_tys.perm)
+    apply (simp only: ty_tys.perm_simps)
     apply (rule a3)
     apply(erule_tac x="(pa + p)" in allE)
     apply simp
@@ -89,7 +89,8 @@
     apply (simp add: fresh_star_def)
     apply clarify
     apply (simp add: fresh_def)
-    apply (simp add: ty_tys_supp)
+    apply(auto)
+    apply (simp add: ty_tys.supp)
     done
   then have "P a (0 \<bullet> t) \<and> P' d (0 \<bullet> ts)" by blast
   then show ?thesis by simp