equal
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172 (auto intro!: add_mono simp add: euclidean_representation_setsum' Ball_def inner_prod_def |
172 (auto intro!: add_mono simp add: euclidean_representation_setsum' Ball_def inner_prod_def |
173 in_Basis_prod_iff inner_Basis_inf_left inner_Basis_sup_left inner_Basis_INF_left Inf_prod_def |
173 in_Basis_prod_iff inner_Basis_inf_left inner_Basis_sup_left inner_Basis_INF_left Inf_prod_def |
174 inner_Basis_SUP_left Sup_prod_def less_prod_def less_eq_prod_def eucl_le[where 'a='a] |
174 inner_Basis_SUP_left Sup_prod_def less_prod_def less_eq_prod_def eucl_le[where 'a='a] |
175 eucl_le[where 'a='b] abs_prod_def abs_inner) |
175 eucl_le[where 'a='b] abs_prod_def abs_inner) |
176 |
176 |
177 text\<open>Instantiation for intervals on @{text ordered_euclidean_space}\<close> |
177 text\<open>Instantiation for intervals on \<open>ordered_euclidean_space\<close>\<close> |
178 |
178 |
179 lemma |
179 lemma |
180 fixes a :: "'a::ordered_euclidean_space" |
180 fixes a :: "'a::ordered_euclidean_space" |
181 shows cbox_interval: "cbox a b = {a..b}" |
181 shows cbox_interval: "cbox a b = {a..b}" |
182 and interval_cbox: "{a..b} = cbox a b" |
182 and interval_cbox: "{a..b} = cbox a b" |