# HG changeset patch # User huffman # Date 1313713922 25200 # Node ID 8766839efb1b90500817338139ae80229d03d1ad # Parent 584a590ce6d3eb456bf771dfc78ab6d8a3e19191 declare euclidean_component_zero[simp] at the point it is proved diff -r 584a590ce6d3 -r 8766839efb1b src/HOL/Multivariate_Analysis/Euclidean_Space.thy --- a/src/HOL/Multivariate_Analysis/Euclidean_Space.thy Thu Aug 18 23:43:22 2011 +0200 +++ b/src/HOL/Multivariate_Analysis/Euclidean_Space.thy Thu Aug 18 17:32:02 2011 -0700 @@ -126,7 +126,7 @@ lemmas isCont_euclidean_component [simp] = bounded_linear.isCont [OF bounded_linear_euclidean_component] -lemma euclidean_component_zero: "0 $$ i = 0" +lemma euclidean_component_zero [simp]: "0 $$ i = 0" unfolding euclidean_component_def by (rule inner_zero_right) lemma euclidean_component_add: "(x + y) $$ i = x $$ i + y $$ i" diff -r 584a590ce6d3 -r 8766839efb1b src/HOL/Multivariate_Analysis/Linear_Algebra.thy --- a/src/HOL/Multivariate_Analysis/Linear_Algebra.thy Thu Aug 18 23:43:22 2011 +0200 +++ b/src/HOL/Multivariate_Analysis/Linear_Algebra.thy Thu Aug 18 17:32:02 2011 -0700 @@ -1756,7 +1756,7 @@ have Kp: "?K > 0" by arith { assume C: "B < 0" have "((\\ i. 1)::'a) \ 0" unfolding euclidean_eq[where 'a='a] - by(auto intro!:exI[where x=0] simp add:euclidean_component_zero) + by(auto intro!:exI[where x=0]) hence "norm ((\\ i. 1)::'a) > 0" by auto with C have "B * norm ((\\ i. 1)::'a) < 0" by (simp add: mult_less_0_iff) diff -r 584a590ce6d3 -r 8766839efb1b src/HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy --- a/src/HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy Thu Aug 18 23:43:22 2011 +0200 +++ b/src/HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy Thu Aug 18 17:32:02 2011 -0700 @@ -5570,9 +5570,6 @@ subsection {* Some properties of a canonical subspace *} -(** move **) -declare euclidean_component_zero[simp] - lemma subspace_substandard: "subspace {x::'a::euclidean_space. (\i x$$i = 0)}" unfolding subspace_def by(auto simp add: euclidean_simps) (* FIXME: duplicate rewrite rule *)