equal
deleted
inserted
replaced
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)" |