--- a/src/HOL/Divides.thy Sun Feb 22 09:52:49 2009 +0100
+++ b/src/HOL/Divides.thy Sun Feb 22 11:30:41 2009 +0100
@@ -178,6 +178,12 @@
lemma dvd_div_mult_self: "a dvd b \<Longrightarrow> (b div a) * a = b"
by (subst (2) mod_div_equality [of b a, symmetric]) (simp add:dvd_imp_mod_0)
+lemma dvd_div_mult: "a dvd b \<Longrightarrow> (b div a) * c = b * c div a"
+apply (cases "a = 0")
+ apply simp
+apply (auto simp: dvd_def mult_assoc)
+done
+
lemma div_dvd_div[simp]:
"a dvd b \<Longrightarrow> a dvd c \<Longrightarrow> (b div a dvd c div a) = (b dvd c)"
apply (cases "a = 0")