src/HOL/Nonstandard_Analysis/HDeriv.thy
changeset 69597 ff784d5a5bfb
parent 69064 5840724b1d71
child 70217 1f04832cbfcf
equal deleted inserted replaced
69596:c8a2755bf220 69597:ff784d5a5bfb
   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"