equal
deleted
inserted
replaced
1023 then obtain k where k: "p = [:k:]" "k \<noteq> 0" |
1023 then obtain k where k: "p = [:k:]" "k \<noteq> 0" |
1024 by (cases p) (simp split: if_splits) |
1024 by (cases p) (simp split: if_splits) |
1025 then have th1: "\<forall>x. poly p x \<noteq> 0" |
1025 then have th1: "\<forall>x. poly p x \<noteq> 0" |
1026 by simp |
1026 by simp |
1027 from k dp(2) have "q ^ (degree p) = p * [:1/k:]" |
1027 from k dp(2) have "q ^ (degree p) = p * [:1/k:]" |
1028 by (simp add: one_poly_def) |
1028 by simp |
1029 then have th2: "p dvd (q ^ (degree p))" .. |
1029 then have th2: "p dvd (q ^ (degree p))" .. |
1030 from dp(1) th1 th2 show ?thesis |
1030 from dp(1) th1 th2 show ?thesis |
1031 by blast |
1031 by blast |
1032 next |
1032 next |
1033 case dp: 3 |
1033 case dp: 3 |