equal
deleted
inserted
replaced
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 |