src/HOL/Multivariate_Analysis/Derivative.thy
changeset 61076 bdc1e2f0a86a
parent 60800 7d04351c795a
child 61104 3c2d4636cebc
equal deleted inserted replaced
61075:f6b0d827240e 61076:bdc1e2f0a86a
  2176   using assms(4-5)
  2176   using assms(4-5)
  2177   unfolding sums_def
  2177   unfolding sums_def
  2178   apply auto
  2178   apply auto
  2179   done
  2179   done
  2180 
  2180 
  2181 text \<open>Considering derivative @{typ "real \<Rightarrow> 'b\<Colon>real_normed_vector"} as a vector.\<close>
  2181 text \<open>Considering derivative @{typ "real \<Rightarrow> 'b::real_normed_vector"} as a vector.\<close>
  2182 
  2182 
  2183 definition "vector_derivative f net = (SOME f'. (f has_vector_derivative f') net)"
  2183 definition "vector_derivative f net = (SOME f'. (f has_vector_derivative f') net)"
  2184 
  2184 
  2185 lemma vector_derivative_unique_at:
  2185 lemma vector_derivative_unique_at:
  2186   assumes "(f has_vector_derivative f') (at x)"
  2186   assumes "(f has_vector_derivative f') (at x)"