src/HOL/Number_Theory/Factorial_Ring.thy
changeset 63539 70d4d9e5707b
parent 63498 a3fe3250d05d
child 63547 00521f181510
--- a/src/HOL/Number_Theory/Factorial_Ring.thy	Thu Jul 21 10:52:27 2016 +0200
+++ b/src/HOL/Number_Theory/Factorial_Ring.thy	Fri Jul 22 08:02:37 2016 +0200
@@ -582,9 +582,9 @@
   from prime_factorization_exists'[OF assms(1)] guess A . note A = this
   moreover from A and assms have "A \<noteq> {#}" by auto
   then obtain x where "x \<in># A" by blast
-  with A(1) have "x dvd msetprod A" "is_prime x" by (auto simp: dvd_msetprod)
-  moreover from this A have "x dvd a" by simp
-  ultimately show ?thesis by blast
+  with A(1) have *: "x dvd msetprod A" "is_prime x" by (auto simp: dvd_msetprod)
+  with A have "x dvd a" by simp
+  with * show ?thesis by blast
 qed
 
 lemma prime_divisors_induct [case_names zero unit factor]: