src/HOL/Number_Theory/Eratosthenes.thy
changeset 62349 7c23469b5118
parent 61762 d50b993b4fb9
child 63040 eb4ddd18d635
equal deleted inserted replaced
62348:9a5f43dac883 62349:7c23469b5118
   281       proof (cases "m = 0")
   281       proof (cases "m = 0")
   282         case True with \<open>m dvd q\<close> show ?thesis by simp
   282         case True with \<open>m dvd q\<close> show ?thesis by simp
   283       next
   283       next
   284         case False with \<open>m \<noteq> 1\<close> have "Suc (Suc 0) \<le> m" by arith
   284         case False with \<open>m \<noteq> 1\<close> have "Suc (Suc 0) \<le> m" by arith
   285         with \<open>m < Suc n\<close> * \<open>m dvd q\<close> have "q dvd m" by simp
   285         with \<open>m < Suc n\<close> * \<open>m dvd q\<close> have "q dvd m" by simp
   286         with \<open>m dvd q\<close> show ?thesis by (simp add: dvd.eq_iff)
   286         with \<open>m dvd q\<close> show ?thesis by (simp add: dvd_antisym)
   287       qed
   287       qed
   288     }
   288     }
   289     then have aux: "\<And>m q. Suc (Suc 0) \<le> q \<Longrightarrow>
   289     then have aux: "\<And>m q. Suc (Suc 0) \<le> q \<Longrightarrow>
   290       q < Suc n \<Longrightarrow>
   290       q < Suc n \<Longrightarrow>
   291       m dvd q \<Longrightarrow>
   291       m dvd q \<Longrightarrow>