# HG changeset patch
# User paulson
# Date 992442591 -7200
# Node ID 2badb9b2a8ec9ea66e1b05b94de84f16c758ee47
# Parent  ef11fb6e6c5894c32608f30c03c1ae895cd3a7b9
New proof of gcd_zero after a change to Divides.ML made the old one fail

diff -r ef11fb6e6c58 -r 2badb9b2a8ec src/HOL/Library/Primes.thy
--- a/src/HOL/Library/Primes.thy	Wed Jun 13 16:28:40 2001 +0200
+++ b/src/HOL/Library/Primes.thy	Wed Jun 13 16:29:51 2001 +0200
@@ -72,17 +72,6 @@
 lemmas gcd_dvd1 [iff] = gcd_dvd_both [THEN conjunct1, standard]
 lemmas gcd_dvd2 [iff] = gcd_dvd_both [THEN conjunct2, standard]
 
-lemma gcd_zero: "(gcd (m, n) = 0) = (m = 0 \<and> n = 0)"
-proof
-  have "gcd (m, n) dvd m \<and> gcd (m, n) dvd n" by simp
-  also assume "gcd (m, n) = 0"
-  finally have "0 dvd m \<and> 0 dvd n" .
-  thus "m = 0 \<and> n = 0" by (simp add: dvd_0_left)
-next
-  assume "m = 0 \<and> n = 0"
-  thus "gcd (m, n) = 0" by simp
-qed
-
 
 text {*
   \medskip Maximality: for all @{term m}, @{term n}, @{term k}
@@ -99,6 +88,9 @@
   apply (blast intro!: gcd_greatest intro: dvd_trans)
   done
 
+lemma gcd_zero: "(gcd (m, n) = 0) = (m = 0 \<and> n = 0)"
+  by (simp only: dvd_0_left_iff [THEN sym] gcd_greatest_iff)
+
 
 text {*
   \medskip Function gcd yields the Greatest Common Divisor.