src/HOL/Algebra/Divisibility.thy
changeset 58247 98d0f85d247f
parent 57865 dcfb33c26f50
child 58889 5b7a9633cfa8
equal deleted inserted replaced
58245:7e54225acef1 58247:98d0f85d247f
  3410           apply (simp, (fast intro: nth_mem[OF len])?)+
  3410           apply (simp, (fast intro: nth_mem[OF len])?)+
  3411     done
  3411     done
  3412 
  3412 
  3413     from len
  3413     from len
  3414       have as': "as' = (take i as' @ as'!i # drop (Suc i) as')"
  3414       have as': "as' = (take i as' @ as'!i # drop (Suc i) as')"
  3415       by (simp add: drop_Suc_conv_tl)
  3415       by (simp add: Cons_nth_drop_Suc)
  3416     with carr
  3416     with carr
  3417       have eer: "essentially_equal G (take i as' @ as'!i # drop (Suc i) as') as'"
  3417       have eer: "essentially_equal G (take i as' @ as'!i # drop (Suc i) as') as'"
  3418       by simp
  3418       by simp
  3419     with v2 afs' carr aa1carr aa2carr nth_mem[OF len]
  3419     with v2 afs' carr aa1carr aa2carr nth_mem[OF len]
  3420       have "aa_1 \<otimes> (as'!i \<otimes> aa_2) \<sim> a"
  3420       have "aa_1 \<otimes> (as'!i \<otimes> aa_2) \<sim> a"