equal
deleted
inserted
replaced
226 lemma NSDERIV_cmult_Id [simp]: "NSDERIV ((*) c) x :> c" |
226 lemma NSDERIV_cmult_Id [simp]: "NSDERIV ((*) c) x :> c" |
227 using NSDERIV_Id [THEN NSDERIV_cmult] by simp |
227 using NSDERIV_Id [THEN NSDERIV_cmult] by simp |
228 |
228 |
229 lemma NSDERIV_inverse: |
229 lemma NSDERIV_inverse: |
230 fixes x :: "'a::real_normed_field" |
230 fixes x :: "'a::real_normed_field" |
231 assumes "x \<noteq> 0" \<comment> \<open>can't get rid of @{term "x \<noteq> 0"} because it isn't continuous at zero\<close> |
231 assumes "x \<noteq> 0" \<comment> \<open>can't get rid of \<^term>\<open>x \<noteq> 0\<close> because it isn't continuous at zero\<close> |
232 shows "NSDERIV (\<lambda>x. inverse x) x :> - (inverse x ^ Suc (Suc 0))" |
232 shows "NSDERIV (\<lambda>x. inverse x) x :> - (inverse x ^ Suc (Suc 0))" |
233 proof - |
233 proof - |
234 { |
234 { |
235 fix h :: "'a star" |
235 fix h :: "'a star" |
236 assume h_Inf: "h \<in> Infinitesimal" |
236 assume h_Inf: "h \<in> Infinitesimal" |