src/HOL/Number_Theory/Eratosthenes.thy
changeset 55337 5d45fb978d5a
parent 55130 70db8d380d62
child 57512 cc97b347b301
equal deleted inserted replaced
55334:5f5104069b33 55337:5d45fb978d5a
   278     q < Suc n \<Longrightarrow>
   278     q < Suc n \<Longrightarrow>
   279     m dvd q \<Longrightarrow>
   279     m dvd q \<Longrightarrow>
   280     \<forall>m\<in>{Suc (Suc 0)..<Suc n}. m dvd q \<longrightarrow> q dvd m \<Longrightarrow>
   280     \<forall>m\<in>{Suc (Suc 0)..<Suc n}. m dvd q \<longrightarrow> q dvd m \<Longrightarrow>
   281     m dvd q \<Longrightarrow> m \<noteq> q \<Longrightarrow> m = 1" by auto
   281     m dvd q \<Longrightarrow> m \<noteq> q \<Longrightarrow> m = 1" by auto
   282   case True then show ?thesis
   282   case True then show ?thesis
   283     apply (auto simp add: numbers_of_marks_sieve numeral_2_eq_2 set_primes_upto dest: prime_gt_Suc_0_nat)
   283     apply (auto simp add: One_nat_def numbers_of_marks_sieve numeral_2_eq_2 set_primes_upto
       
   284         dest: prime_gt_Suc_0_nat)
   284     apply (metis One_nat_def Suc_le_eq less_not_refl prime_nat_def)
   285     apply (metis One_nat_def Suc_le_eq less_not_refl prime_nat_def)
   285     apply (metis One_nat_def Suc_le_eq aux prime_nat_def)
   286     apply (metis One_nat_def Suc_le_eq aux prime_nat_def)
   286     done
   287     done
   287 qed
   288 qed
   288 
   289