# HG changeset patch # User huffman # Date 1379001832 25200 # Node ID a7bcbb5a17d8455ccea445d291cf5a88c50b551d # Parent b6dc5403cad1188effc89c327c15b23c32151836 removed outdated comments diff -r b6dc5403cad1 -r a7bcbb5a17d8 src/HOL/Multivariate_Analysis/Cartesian_Euclidean_Space.thy --- a/src/HOL/Multivariate_Analysis/Cartesian_Euclidean_Space.thy Fri Sep 13 00:55:44 2013 +0200 +++ b/src/HOL/Multivariate_Analysis/Cartesian_Euclidean_Space.thy Thu Sep 12 09:03:52 2013 -0700 @@ -322,7 +322,6 @@ shows "setsum (\x. c *s f x) S = c *s setsum f S" by (simp add: vec_eq_iff setsum_right_distrib) -(* TODO: use setsum_norm_allsubsets_bound *) lemma setsum_norm_allsubsets_bound_cart: fixes f:: "'a \ real ^'n" assumes fP: "finite P" and fPs: "\Q. Q \ P \ norm (setsum f Q) \ e" diff -r b6dc5403cad1 -r a7bcbb5a17d8 src/HOL/Multivariate_Analysis/Path_Connected.thy --- a/src/HOL/Multivariate_Analysis/Path_Connected.thy Fri Sep 13 00:55:44 2013 +0200 +++ b/src/HOL/Multivariate_Analysis/Path_Connected.thy Thu Sep 12 09:03:52 2013 -0700 @@ -587,7 +587,7 @@ qed lemma open_path_component: - fixes s :: "'a::real_normed_vector set" (*TODO: generalize to metric_space*) + fixes s :: "'a::real_normed_vector set" assumes "open s" shows "open {y. path_component s x y}" unfolding open_contains_ball @@ -620,7 +620,7 @@ qed lemma open_non_path_component: - fixes s :: "'a::real_normed_vector set" (*TODO: generalize to metric_space*) + fixes s :: "'a::real_normed_vector set" assumes "open s" shows "open(s - {y. path_component s x y})" unfolding open_contains_ball @@ -648,7 +648,7 @@ qed lemma connected_open_path_connected: - fixes s :: "'a::real_normed_vector set" (*TODO: generalize to metric_space*) + fixes s :: "'a::real_normed_vector set" assumes "open s" "connected s" shows "path_connected s" unfolding path_connected_component_set