equal
deleted
inserted
replaced
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) |