src/HOL/GCD.thy
changeset 30082 43c5b7bfc791
parent 30042 31039ee583fa
child 30242 aea5d7fa7ef5
--- a/src/HOL/GCD.thy	Tue Feb 24 11:10:05 2009 -0800
+++ b/src/HOL/GCD.thy	Tue Feb 24 11:12:58 2009 -0800
@@ -60,9 +60,12 @@
 lemma gcd_non_0: "n > 0 \<Longrightarrow> gcd m n = gcd n (m mod n)"
   by simp
 
-lemma gcd_1 [simp, algebra]: "gcd m (Suc 0) = 1"
+lemma gcd_1 [simp, algebra]: "gcd m (Suc 0) = Suc 0"
   by simp
 
+lemma nat_gcd_1_right [simp, algebra]: "gcd m 1 = 1"
+  unfolding One_nat_def by (rule gcd_1)
+
 declare gcd.simps [simp del]
 
 text {*
@@ -116,9 +119,12 @@
   apply (blast intro: dvd_trans)
   done
 
-lemma gcd_1_left [simp, algebra]: "gcd (Suc 0) m = 1"
+lemma gcd_1_left [simp, algebra]: "gcd (Suc 0) m = Suc 0"
   by (simp add: gcd_commute)
 
+lemma nat_gcd_1_left [simp, algebra]: "gcd 1 m = 1"
+  unfolding One_nat_def by (rule gcd_1_left)
+
 text {*
   \medskip Multiplication laws
 *}