--- a/src/HOL/Int.thy Wed Dec 03 20:24:17 2008 -0800
+++ b/src/HOL/Int.thy Wed Dec 03 20:45:42 2008 -0800
@@ -1299,13 +1299,21 @@
text {* Simplification of relational operations *}
+lemma less_number_of [simp]:
+ "(number_of x::'a::{ordered_idom,number_ring}) < number_of y \<longleftrightarrow> x < y"
+ unfolding number_of_eq by (rule of_int_less_iff)
+
+lemma le_number_of [simp]:
+ "(number_of x::'a::{ordered_idom,number_ring}) \<le> number_of y \<longleftrightarrow> x \<le> y"
+ unfolding number_of_eq by (rule of_int_le_iff)
+
lemmas rel_simps [simp] =
+ less_number_of less_bin_simps
+ le_number_of le_bin_simps
eq_number_of_eq iszero_0 nonzero_number_of_Min
iszero_number_of_Bit0 iszero_number_of_Bit1
- less_number_of_eq_neg
not_neg_number_of_Pls not_neg_0 not_neg_1 not_iszero_1
neg_number_of_Min neg_number_of_Bit0 neg_number_of_Bit1
- le_number_of_eq
(* iszero_number_of_Pls would never be used
because its lhs simplifies to "iszero 0" *)