# HG changeset patch
# User haftmann
# Date 1268204679 -3600
# Node ID 2fa645db6e58446d2fd348c64e2055b7949b4c8b
# Parent  97b94dc975c7b3081cfe7556664814cc30ade869
tuned

diff -r 97b94dc975c7 -r 2fa645db6e58 src/HOL/ex/Transfer_Ex.thy
--- a/src/HOL/ex/Transfer_Ex.thy	Tue Mar 09 21:19:49 2010 +0100
+++ b/src/HOL/ex/Transfer_Ex.thy	Wed Mar 10 08:04:39 2010 +0100
@@ -2,41 +2,46 @@
 header {* Various examples for transfer procedure *}
 
 theory Transfer_Ex
-imports Complex_Main
+imports Main
 begin
 
-(* nat to int *)
-
 lemma ex1: "(x::nat) + y = y + x"
   by auto
 
-thm ex1 [transferred]
+lemma "(0\<Colon>int) \<le> (y\<Colon>int) \<Longrightarrow> (0\<Colon>int) \<le> (x\<Colon>int) \<Longrightarrow> x + y = y + x"
+  by (fact ex1 [transferred])
 
 lemma ex2: "(a::nat) div b * b + a mod b = a"
   by (rule mod_div_equality)
 
-thm ex2 [transferred]
+lemma "(0\<Colon>int) \<le> (b\<Colon>int) \<Longrightarrow> (0\<Colon>int) \<le> (a\<Colon>int) \<Longrightarrow> a div b * b + a mod b = a"
+  by (fact ex2 [transferred])
 
 lemma ex3: "ALL (x::nat). ALL y. EX z. z >= x + y"
   by auto
 
-thm ex3 [transferred natint]
+lemma "\<forall>x\<ge>0\<Colon>int. \<forall>y\<ge>0\<Colon>int. \<exists>xa\<ge>0\<Colon>int. x + y \<le> xa"
+  by (fact ex3 [transferred nat_int])
 
 lemma ex4: "(x::nat) >= y \<Longrightarrow> (x - y) + y = x"
   by auto
 
-thm ex4 [transferred]
+lemma "(0\<Colon>int) \<le> (x\<Colon>int) \<Longrightarrow> (0\<Colon>int) \<le> (y\<Colon>int) \<Longrightarrow> y \<le> x \<Longrightarrow> tsub x y + y = x"
+  by (fact ex4 [transferred])
 
-lemma ex5: "(2::nat) * (SUM i <= n. i) = n * (n + 1)"
+lemma ex5: "(2::nat) * \<Sum>{..n} = n * (n + 1)"
   by (induct n rule: nat_induct, auto)
 
-thm ex5 [transferred]
+lemma "(0\<Colon>int) \<le> (n\<Colon>int) \<Longrightarrow> (2\<Colon>int) * \<Sum>{0\<Colon>int..n} = n * (n + (1\<Colon>int))"
+  by (fact ex5 [transferred])
+
+lemma "(0\<Colon>nat) \<le> (n\<Colon>nat) \<Longrightarrow> (2\<Colon>nat) * \<Sum>{0\<Colon>nat..n} = n * (n + (1\<Colon>nat))"
+  by (fact ex5 [transferred, transferred])
 
 theorem ex6: "0 <= (n::int) \<Longrightarrow> 2 * \<Sum>{0..n} = n * (n + 1)"
   by (rule ex5 [transferred])
 
-thm ex6 [transferred]
-
-thm ex5 [transferred, transferred]
+lemma "(0\<Colon>nat) \<le> (n\<Colon>nat) \<Longrightarrow> (2\<Colon>nat) * \<Sum>{0\<Colon>nat..n} = n * (n + (1\<Colon>nat))"
+  by (fact ex6 [transferred])
 
 end
\ No newline at end of file