src/HOL/Algebra/abstract/Ideal2.thy
changeset 42793 88bee9f6eec7
parent 42768 4db4a8b164c1
child 44174 d1d79f0e1ea6
equal deleted inserted replaced
42792:85fb70b0c5e8 42793:88bee9f6eec7
   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)