# HG changeset patch # User nipkow # Date 1572977700 -3600 # Node ID fdb6c5034c24c7d367ff718e15369c702eb5ddbd # Parent ddd4aefc540f9f121c807711198014d089d199d9# Parent 9d2753406c605002d06a0d1c565eb3fe6bb74b7a merged diff -r ddd4aefc540f -r fdb6c5034c24 src/HOL/Analysis/Convex.thy --- a/src/HOL/Analysis/Convex.thy Tue Nov 05 10:02:09 2019 -0500 +++ b/src/HOL/Analysis/Convex.thy Tue Nov 05 19:15:00 2019 +0100 @@ -2696,8 +2696,7 @@ proof - obtain s u where s_u: "finite s \ s \ {} \ s \ S \ sum u s = 1 \ (\v\s. u v *\<^sub>R v) = 0" using assms affine_hull_explicit[of S] by auto - then have "\v\s. u v \ 0" - using sum_not_0[of "u" "s"] by auto + then have "\v\s. u v \ 0" by auto then have "finite s \ s \ S \ (\v\s. u v \ 0 \ (\v\s. u v *\<^sub>R v) = 0)" using s_u by auto then show ?thesis @@ -3483,7 +3482,7 @@ have "sum c s = 0" by (simp add: c_def comm_monoid_add_class.sum.If_cases \finite s\ sum_negf) moreover have "\ (\v\s. c v = 0)" - by (metis (no_types) IntD1 \s \ t = t\ a1 c_def sum_not_0 zero_neq_one) + by (metis (no_types) IntD1 \s \ t = t\ a1 c_def sum.neutral zero_neq_one) moreover have "(\v\s. c v *\<^sub>R v) = 0" by (simp add: c_def if_smult sum_negf comm_monoid_add_class.sum.If_cases \finite s\) diff -r ddd4aefc540f -r fdb6c5034c24 src/HOL/Analysis/Linear_Algebra.thy --- a/src/HOL/Analysis/Linear_Algebra.thy Tue Nov 05 10:02:09 2019 -0500 +++ b/src/HOL/Analysis/Linear_Algebra.thy Tue Nov 05 19:15:00 2019 +0100 @@ -50,9 +50,6 @@ lemma independent_substdbasis: "d \ Basis \ independent d" by (rule independent_mono[OF independent_Basis]) -lemma sum_not_0: "sum f A \ 0 \ \a \ A. f a \ 0" - by (rule ccontr) auto - lemma subset_translation_eq [simp]: fixes a :: "'a::real_vector" shows "(+) a ` s \ (+) a ` t \ s \ t" by auto