src/HOL/Analysis/FPS_Convergence.thy
changeset 68046 6aba668aea78
parent 66480 4b8d1df8933b
child 68403 223172b97d0b
equal deleted inserted replaced
68041:d45b78cb86cf 68046:6aba668aea78
   269   unfolding fps_conv_radius_def by (simp add: conv_radius_cmult_right)
   269   unfolding fps_conv_radius_def by (simp add: conv_radius_cmult_right)
   270 
   270 
   271 lemma fps_conv_radius_uminus [simp]:
   271 lemma fps_conv_radius_uminus [simp]:
   272   "fps_conv_radius (-f) = fps_conv_radius f"
   272   "fps_conv_radius (-f) = fps_conv_radius f"
   273   using fps_conv_radius_cmult_left[of "-1" f]
   273   using fps_conv_radius_cmult_left[of "-1" f]
   274   by (simp add: fps_const_neg [symmetric] del: fps_const_neg)
   274   by (simp reorient: fps_const_neg)
   275 
   275 
   276 lemma fps_conv_radius_add: "fps_conv_radius (f + g) \<ge> min (fps_conv_radius f) (fps_conv_radius g)"
   276 lemma fps_conv_radius_add: "fps_conv_radius (f + g) \<ge> min (fps_conv_radius f) (fps_conv_radius g)"
   277   unfolding fps_conv_radius_def using conv_radius_add_ge[of "fps_nth f" "fps_nth g"]
   277   unfolding fps_conv_radius_def using conv_radius_add_ge[of "fps_nth f" "fps_nth g"]
   278   by simp
   278   by simp
   279 
   279