equal
deleted
inserted
replaced
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 |