src/HOL/Multivariate_Analysis/Ordered_Euclidean_Space.thy
changeset 61808 fc1556774cfe
parent 61694 6571c78c9667
child 61945 1135b8de26c3
equal deleted inserted replaced
61807:965769fe2b63 61808:fc1556774cfe
   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"