equal
deleted
inserted
replaced
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> |