src/HOL/Algebra/Divisibility.thy
changeset 75455 91c16c5ad3e9
parent 73706 4b1386b2c23e
child 80914 d97fdabd9e2b
equal deleted inserted replaced
75454:295e1c9d2994 75455:91c16c5ad3e9
  2598   then show ?case
  2598   then show ?case
  2599     by simp (meson Units_one_closed aprime carr divides_unit primeE)
  2599     by simp (meson Units_one_closed aprime carr divides_unit primeE)
  2600 next
  2600 next
  2601   case (Cons x as)
  2601   case (Cons x as)
  2602   then have "x \<in> carrier G"  "set as \<subseteq> carrier G" and "a divides x \<otimes> foldr (\<otimes>) as \<one>"
  2602   then have "x \<in> carrier G"  "set as \<subseteq> carrier G" and "a divides x \<otimes> foldr (\<otimes>) as \<one>"
  2603     by (auto simp: )
  2603     by auto
  2604   with carr aprime have "a divides x \<or> a divides foldr (\<otimes>) as \<one>"
  2604   with carr aprime have "a divides x \<or> a divides foldr (\<otimes>) as \<one>"
  2605     by (intro prime_divides) simp+
  2605     by (intro prime_divides) simp+
  2606   then show ?case
  2606   then show ?case
  2607     using Cons.IH Cons.prems(1) by force
  2607     using Cons.IH Cons.prems(1) by force
  2608 qed
  2608 qed