src/HOL/Computational_Algebra/Fundamental_Theorem_Algebra.thy
changeset 65486 d801126a14cb
parent 65435 378175f44328
child 66447 a1f5c5c26fa6
equal deleted inserted replaced
65485:8c7bc3a13513 65486:d801126a14cb
  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