src/HOL/Analysis/Henstock_Kurzweil_Integration.thy
changeset 71174 7fac205dd737
parent 71172 575b3a818de5
child 71192 a8ccea88b725
equal deleted inserted replaced
71173:caede3159e23 71174:7fac205dd737
  3490       done
  3490       done
  3491     moreover from True have *: "\<And>i. (m *\<^sub>R b + c) \<bullet> i - (m *\<^sub>R a + c) \<bullet> i = m *\<^sub>R (b-a) \<bullet> i"
  3491     moreover from True have *: "\<And>i. (m *\<^sub>R b + c) \<bullet> i - (m *\<^sub>R a + c) \<bullet> i = m *\<^sub>R (b-a) \<bullet> i"
  3492       by (simp add: inner_simps field_simps)
  3492       by (simp add: inner_simps field_simps)
  3493     ultimately show ?thesis
  3493     ultimately show ?thesis
  3494       by (simp add: image_affinity_cbox True content_cbox'
  3494       by (simp add: image_affinity_cbox True content_cbox'
  3495         prod.distrib prod_constant inner_diff_left)
  3495         prod.distrib inner_diff_left)
  3496   next
  3496   next
  3497     case False
  3497     case False
  3498     with \<open>cbox a b \<noteq> {}\<close> have "cbox (m *\<^sub>R b + c) (m *\<^sub>R a + c) \<noteq> {}"
  3498     with \<open>cbox a b \<noteq> {}\<close> have "cbox (m *\<^sub>R b + c) (m *\<^sub>R a + c) \<noteq> {}"
  3499       unfolding box_ne_empty
  3499       unfolding box_ne_empty
  3500       apply (intro ballI)
  3500       apply (intro ballI)