src/HOL/Analysis/Derivative.thy
changeset 64240 eabf80376aab
parent 64008 17a20ca86d62
child 64267 b9a1486e79be
equal deleted inserted replaced
64239:de5cd9217d4c 64240:eabf80376aab
   696   then obtain x where
   696   then obtain x where
   697     "x \<in> {a <..< b}"
   697     "x \<in> {a <..< b}"
   698     "(\<lambda>xa. f' x xa - (f b - f a) / (b - a) * xa) = (\<lambda>v. 0)" ..
   698     "(\<lambda>xa. f' x xa - (f b - f a) / (b - a) * xa) = (\<lambda>v. 0)" ..
   699   then show ?thesis
   699   then show ?thesis
   700     by (metis (hide_lams) assms(1) diff_gt_0_iff_gt eq_iff_diff_eq_0
   700     by (metis (hide_lams) assms(1) diff_gt_0_iff_gt eq_iff_diff_eq_0
   701       zero_less_mult_iff nonzero_mult_divide_cancel_right not_real_square_gt_zero
   701       zero_less_mult_iff nonzero_mult_div_cancel_right not_real_square_gt_zero
   702       times_divide_eq_left)
   702       times_divide_eq_left)
   703 qed
   703 qed
   704 
   704 
   705 lemma mvt_simple:
   705 lemma mvt_simple:
   706   fixes f :: "real \<Rightarrow> real"
   706   fixes f :: "real \<Rightarrow> real"