# HG changeset patch
# User Cezary Kaliszyk <kaliszyk@in.tum.de>
# Date 1269331997 -3600
# Node ID a7e60da429e27832c55ecf2f54f3be33d4cc467c
# Parent  5f0bb35114c35539ecd062e617701cf394525bb7
Move Let properties to ExLet

diff -r 5f0bb35114c3 -r a7e60da429e2 Nominal/ExLet.thy
--- a/Nominal/ExLet.thy	Tue Mar 23 09:06:28 2010 +0100
+++ b/Nominal/ExLet.thy	Tue Mar 23 09:13:17 2010 +0100
@@ -11,15 +11,15 @@
   Vr "name"
 | Ap "trm" "trm"
 | Lm x::"name" t::"trm"  bind x in t
-| Lt a::"lts" t::"trm"   bind "bv a" in t
+| Lt a::"lts" t::"trm"   bind "bn a" in t
 and lts =
-  Nil
-| Cons "name" "trm" "lts"
+  Lnil
+| Lcons "name" "trm" "lts"
 binder
   bn
 where
-  "bn Nil = {}"
-| "bn (Cons x t l) = {atom x} \<union> (bn l)"
+  "bn Lnil = {}"
+| "bn (Lcons x t l) = {atom x} \<union> (bn l)"
 
 thm trm_lts.fv
 thm trm_lts.eq_iff
@@ -29,6 +29,43 @@
 thm trm_lts.distinct
 thm trm_lts.fv[simplified trm_lts.supp]
 
+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))"
+  by (simp add: trm_lts.eq_iff)
+
+lemma lets_ok:
+  "(Lt (Lcons x (Vr y) 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)
+  apply (simp add: fresh_star_def eqvts)
+  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
+
+
+lemma lets_not_ok1:
+  "(Lt (Lcons x (Vr x) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) =
+   (Lt (Lcons y (Vr x) (Lcons x (Vr y) Lnil)) (Ap (Vr x) (Vr y)))"
+  apply (simp add: alphas trm_lts.eq_iff)
+  apply (rule_tac x="0::perm" in exI)
+  apply (simp add: fresh_star_def eqvts)
+  apply blast
+  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
+
+
 end
 
 
diff -r 5f0bb35114c3 -r a7e60da429e2 Nominal/Manual/Term5n.thy
--- a/Nominal/Manual/Term5n.thy	Tue Mar 23 09:06:28 2010 +0100
+++ b/Nominal/Manual/Term5n.thy	Tue Mar 23 09:13:17 2010 +0100
@@ -174,55 +174,4 @@
 lemmas fv_lts[simp] = fv_rlts.simps[quot_lifted]
 lemmas alpha5_INJ = alpha5_inj[unfolded alpha_gen, quot_lifted, folded alpha_gen]
 
-lemma lets_bla:
-  "x \<noteq> z \<Longrightarrow> y \<noteq> z \<Longrightarrow> x \<noteq> y \<Longrightarrow>(Lt5 (Lcons x (Vr5 y) Lnil) (Vr5 x)) \<noteq> (Lt5 (Lcons x (Vr5 z) Lnil) (Vr5 x))"
-apply (simp only: alpha5_INJ)
-apply (simp only: bv5)
-apply simp
-done
-
-lemma lets_ok:
-  "(Lt5 (Lcons x (Vr5 y) Lnil) (Vr5 x)) = (Lt5 (Lcons y (Vr5 y) Lnil) (Vr5 y))"
-apply (simp add: alpha5_INJ)
-apply (rule_tac x="(x \<leftrightarrow> y)" in exI)
-apply (simp_all add: alpha_gen)
-apply (simp add: permute_trm5_lts fresh_star_def eqvts)
-done
-
-lemma lets_ok3:
-  "x \<noteq> y \<Longrightarrow>
-   (Lt5 (Lcons x (Ap5 (Vr5 y) (Vr5 x)) (Lcons y (Vr5 y) Lnil)) (Ap5 (Vr5 x) (Vr5 y))) \<noteq>
-   (Lt5 (Lcons y (Ap5 (Vr5 x) (Vr5 y)) (Lcons x (Vr5 x) Lnil)) (Ap5 (Vr5 x) (Vr5 y)))"
-apply (simp add: permute_trm5_lts alpha_gen alpha5_INJ)
-done
-
-
-lemma lets_not_ok1:
-  "(Lt5 (Lcons x (Vr5 x) (Lcons y (Vr5 y) Lnil)) (Ap5 (Vr5 x) (Vr5 y))) =
-   (Lt5 (Lcons y (Vr5 x) (Lcons x (Vr5 y) Lnil)) (Ap5 (Vr5 x) (Vr5 y)))"
-apply (simp add: alpha5_INJ alpha_gen)
-apply (rule_tac x="0::perm" in exI)
-apply (simp add: permute_trm5_lts fresh_star_def alpha5_INJ(5) alpha5_INJ(2) alpha5_INJ(1) eqvts)
-apply blast
-done
-
-lemma distinct_helper:
-  shows "\<not>(rVr5 x \<approx>5 rAp5 y z)"
-  apply auto
-  apply (erule alpha_rtrm5.cases)
-  apply (simp_all only: rtrm5.distinct)
-  done
-
-lemma distinct_helper2:
-  shows "(Vr5 x) \<noteq> (Ap5 y z)"
-  by (lifting distinct_helper)
-
-lemma lets_nok:
-  "x \<noteq> y \<Longrightarrow> x \<noteq> z \<Longrightarrow> z \<noteq> y \<Longrightarrow>
-   (Lt5 (Lcons x (Ap5 (Vr5 z) (Vr5 z)) (Lcons y (Vr5 z) Lnil)) (Ap5 (Vr5 x) (Vr5 y))) \<noteq>
-   (Lt5 (Lcons y (Vr5 z) (Lcons x (Ap5 (Vr5 z) (Vr5 z)) Lnil)) (Ap5 (Vr5 x) (Vr5 y)))"
-apply (simp only: alpha5_INJ(3) alpha5_INJ(5) alpha_gen permute_trm5_lts fresh_star_def)
-apply (simp add: distinct_helper2 alpha5_INJ permute_trm5_lts)
-done
-
 end