--- a/src/HOL/Ring_and_Field.thy Thu Nov 09 00:19:16 2006 +0100
+++ b/src/HOL/Ring_and_Field.thy Thu Nov 09 00:43:12 2006 +0100
@@ -510,6 +510,13 @@
apply (erule mult_left_mono, assumption)
done
+lemma mult_mono':
+ "[|a \<le> b; c \<le> d; 0 \<le> a; 0 \<le> c|]
+ ==> a * c \<le> b * (d::'a::pordered_semiring)"
+apply (rule mult_mono)
+apply (fast intro: order_trans)+
+done
+
lemma less_1_mult: "[| 1 < m; 1 < n |] ==> 1 < m*(n::'a::ordered_semidom)"
apply (insert mult_strict_mono [of 1 m 1 n])
apply (simp add: order_less_trans [OF zero_less_one])