src/HOL/MacLaurin.thy
changeset 61799 4cf66f21b764
parent 61609 77b453bd616f
child 61944 5d06ecfdb472
equal deleted inserted replaced
61798:27f3c10b0b50 61799:4cf66f21b764
   207   and DERIV: "\<forall>m t. m < n & h \<le> t & t \<le> 0 --> DERIV (diff m) t :> diff (Suc m) t"
   207   and DERIV: "\<forall>m t. m < n & h \<le> t & t \<le> 0 --> DERIV (diff m) t :> diff (Suc m) t"
   208   shows "\<exists>t. h < t & t < 0 &
   208   shows "\<exists>t. h < t & t < 0 &
   209          f h = (\<Sum>m<n. diff m 0 / (fact m) * h ^ m) +
   209          f h = (\<Sum>m<n. diff m 0 / (fact m) * h ^ m) +
   210          diff n t / (fact n) * h ^ n"
   210          diff n t / (fact n) * h ^ n"
   211 proof -
   211 proof -
   212   txt "Transform @{text ABL'} into @{text derivative_intros} format."
   212   txt "Transform \<open>ABL'\<close> into \<open>derivative_intros\<close> format."
   213   note DERIV' = DERIV_chain'[OF _ DERIV[rule_format], THEN DERIV_cong]
   213   note DERIV' = DERIV_chain'[OF _ DERIV[rule_format], THEN DERIV_cong]
   214   from assms
   214   from assms
   215   have "\<exists>t>0. t < - h \<and>
   215   have "\<exists>t>0. t < - h \<and>
   216     f (- (- h)) =
   216     f (- (- h)) =
   217     (\<Sum>m<n.
   217     (\<Sum>m<n.