equal
deleted
inserted
replaced
274 |
274 |
275 lemma pid_irred_imp_prime: "irred a ==> prime (a::'a::pid)" |
275 lemma pid_irred_imp_prime: "irred a ==> prime (a::'a::pid)" |
276 apply (unfold prime_def) |
276 apply (unfold prime_def) |
277 apply (rule conjI) |
277 apply (rule conjI) |
278 apply (rule_tac [2] conjI) |
278 apply (rule_tac [2] conjI) |
279 apply (tactic "clarify_tac @{claset} 3") |
279 apply (tactic "clarify_tac @{context} 3") |
280 apply (drule_tac [3] I = "ideal_of {a, b}" and x = "1" in irred_imp_max_ideal) |
280 apply (drule_tac [3] I = "ideal_of {a, b}" and x = "1" in irred_imp_max_ideal) |
281 apply (auto intro: ideal_of_is_ideal pid_ax simp add: irred_def not_dvd_psubideal pid_ax) |
281 apply (auto intro: ideal_of_is_ideal pid_ax simp add: irred_def not_dvd_psubideal pid_ax) |
282 apply (simp add: ideal_of_2_structure) |
282 apply (simp add: ideal_of_2_structure) |
283 apply clarify |
283 apply clarify |
284 apply (drule_tac f = "op* aa" in arg_cong) |
284 apply (drule_tac f = "op* aa" in arg_cong) |