# HG changeset patch
# User haftmann
# Date 1222412991 -7200
# Node ID 10ea34297962690e020a2da9ee0511a6c599ba00
# Parent  a75d4551ee008983133a78cfe0a047c5a2f53035
op = vs. eq

diff -r a75d4551ee00 -r 10ea34297962 src/HOL/ex/Numeral.thy
--- a/src/HOL/ex/Numeral.thy	Thu Sep 25 20:34:21 2008 +0200
+++ b/src/HOL/ex/Numeral.thy	Fri Sep 26 09:09:51 2008 +0200
@@ -800,7 +800,7 @@
   "(uminus :: int \<Rightarrow> int) = uminus"
   "(op - :: int \<Rightarrow> int \<Rightarrow> int) = op -"
   "(op * :: int \<Rightarrow> int \<Rightarrow> int) = op *"
-  "(op = :: int \<Rightarrow> int \<Rightarrow> bool) = op ="
+  "(eq_class.eq :: int \<Rightarrow> int \<Rightarrow> bool) = eq_class.eq"
   "(op \<le> :: int \<Rightarrow> int \<Rightarrow> bool) = op \<le>"
   "(op < :: int \<Rightarrow> int \<Rightarrow> bool) = op <"
   by rule+
@@ -843,17 +843,17 @@
   by (simp_all add: of_num_times [symmetric])
 
 lemma eq_int_code [code]:
-  "0 = (0::int) \<longleftrightarrow> True"
-  "0 = Pls l \<longleftrightarrow> False"
-  "0 = Mns l \<longleftrightarrow> False"
-  "Pls k = 0 \<longleftrightarrow> False"
-  "Pls k = Pls l \<longleftrightarrow> k = l"
-  "Pls k = Mns l \<longleftrightarrow> False"
-  "Mns k = 0 \<longleftrightarrow> False"
-  "Mns k = Pls l \<longleftrightarrow> False"
-  "Mns k = Mns l \<longleftrightarrow> k = l"
+  "eq_class.eq 0 (0::int) \<longleftrightarrow> True"
+  "eq_class.eq 0 (Pls l) \<longleftrightarrow> False"
+  "eq_class.eq 0 (Mns l) \<longleftrightarrow> False"
+  "eq_class.eq (Pls k) 0 \<longleftrightarrow> False"
+  "eq_class.eq (Pls k) (Pls l) \<longleftrightarrow> eq_class.eq k l"
+  "eq_class.eq (Pls k) (Mns l) \<longleftrightarrow> False"
+  "eq_class.eq (Mns k) 0 \<longleftrightarrow> False"
+  "eq_class.eq (Mns k) (Pls l) \<longleftrightarrow> False"
+  "eq_class.eq (Mns k) (Mns l) \<longleftrightarrow> eq_class.eq k l"
   using of_num_pos [of l, where ?'a = int] of_num_pos [of k, where ?'a = int]
-  by (simp_all add: of_num_eq_iff)
+  by (simp_all add: of_num_eq_iff eq)
 
 lemma less_eq_int_code [code]:
   "0 \<le> (0::int) \<longleftrightarrow> True"