author paulson Wed, 13 Jun 2001 16:29:51 +0200 changeset 11374 2badb9b2a8ec parent 11373 ef11fb6e6c58 child 11375 a6730c90e753
New proof of gcd_zero after a change to Divides.ML made the old one fail
--- 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.