# HG changeset patch # User huffman # Date 1314311754 25200 # Node ID bf8014b4f9333c7d76b02f38ce06c550608affa0 # Parent abcf7c0743e8a6704c1c2eeb83768200bdef68dd remove dot_lsum and dot_rsum in favor of inner_setsum_{left,right} diff -r abcf7c0743e8 -r bf8014b4f933 NEWS --- a/NEWS Thu Aug 25 14:26:38 2011 -0700 +++ b/NEWS Thu Aug 25 15:35:54 2011 -0700 @@ -218,6 +218,8 @@ Lim_linear ~> bounded_linear.tendsto Lim_component ~> tendsto_euclidean_component Lim_component_cart ~> tendsto_vec_nth + dot_lsum ~> inner_setsum_left + dot_rsum ~> inner_setsum_right subset_interior ~> interior_mono subset_closure ~> closure_mono closure_univ ~> closure_UNIV diff -r abcf7c0743e8 -r bf8014b4f933 src/HOL/Multivariate_Analysis/Linear_Algebra.thy --- a/src/HOL/Multivariate_Analysis/Linear_Algebra.thy Thu Aug 25 14:26:38 2011 -0700 +++ b/src/HOL/Multivariate_Analysis/Linear_Algebra.thy Thu Aug 25 15:35:54 2011 -0700 @@ -191,12 +191,6 @@ apply (rule setsum_mono_zero_right[OF fT fST]) by (auto intro: setsum_0') -lemma dot_lsum: "finite S \ setsum f S \ y = setsum (\x. f x \ y) S " - apply(induct rule: finite_induct) by(auto simp add: inner_add) - -lemma dot_rsum: "finite S \ y \ setsum f S = setsum (\x. y \ f x) S " - apply(induct rule: finite_induct) by(auto simp add: inner_add) - lemma vector_eq_ldot: "(\x. x \ y = x \ z) \ y = z" proof assume "\x. x \ y = x \ z" @@ -1816,7 +1810,7 @@ apply (subst Cy) using C(1) fth apply (simp only: setsum_clauses) - apply (auto simp add: inner_add inner_commute[of y a] dot_lsum[OF fth]) + apply (auto simp add: inner_add inner_commute[of y a] inner_setsum_left) apply (rule setsum_0') apply clarsimp apply (rule C(4)[unfolded pairwise_def orthogonal_def, rule_format]) @@ -1833,7 +1827,7 @@ using C(1) fth apply (simp only: setsum_clauses) apply (subst inner_commute[of x]) - apply (auto simp add: inner_add inner_commute[of x a] dot_rsum[OF fth]) + apply (auto simp add: inner_add inner_commute[of x a] inner_setsum_right) apply (rule setsum_0') apply clarsimp apply (rule C(4)[unfolded pairwise_def orthogonal_def, rule_format]) @@ -1903,7 +1897,7 @@ apply (subst B') using fB fth unfolding setsum_clauses(2)[OF fth] apply simp unfolding inner_simps - apply (clarsimp simp add: inner_add dot_lsum) + apply (clarsimp simp add: inner_add inner_setsum_left) apply (rule setsum_0', rule ballI) unfolding inner_commute by (auto simp add: x field_simps intro: B(5)[unfolded pairwise_def orthogonal_def, rule_format])}