--- a/src/HOL/Divides.thy Thu Mar 12 00:02:30 2009 +0100
+++ b/src/HOL/Divides.thy Thu Mar 12 15:31:26 2009 +0100
@@ -295,6 +295,27 @@
end
+lemma div_mult_div_if_dvd: "(y::'a::{semiring_div,no_zero_divisors}) dvd x \<Longrightarrow>
+ z dvd w \<Longrightarrow> (x div y) * (w div z) = (x * w) div (y * z)"
+unfolding dvd_def
+ apply clarify
+ apply (case_tac "y = 0")
+ apply simp
+ apply (case_tac "z = 0")
+ apply simp
+ apply (simp add: algebra_simps)
+ apply (subst mult_assoc [symmetric])
+ apply (simp add: no_zero_divisors)
+done
+
+
+lemma div_power: "(y::'a::{semiring_div,no_zero_divisors,recpower}) dvd x \<Longrightarrow>
+ (x div y)^n = x^n div y^n"
+apply (induct n)
+ apply simp
+apply(simp add: div_mult_div_if_dvd dvd_power_same)
+done
+
class ring_div = semiring_div + comm_ring_1
begin