1.1 --- a/src/HOL/Multivariate_Analysis/Euclidean_Space.thy Thu Aug 18 23:43:22 2011 +0200
1.2 +++ b/src/HOL/Multivariate_Analysis/Euclidean_Space.thy Thu Aug 18 17:32:02 2011 -0700
1.3 @@ -126,7 +126,7 @@
1.4 lemmas isCont_euclidean_component [simp] =
1.5 bounded_linear.isCont [OF bounded_linear_euclidean_component]
1.6
1.7 -lemma euclidean_component_zero: "0 $$ i = 0"
1.8 +lemma euclidean_component_zero [simp]: "0 $$ i = 0"
1.9 unfolding euclidean_component_def by (rule inner_zero_right)
1.10
1.11 lemma euclidean_component_add: "(x + y) $$ i = x $$ i + y $$ i"
2.1 --- a/src/HOL/Multivariate_Analysis/Linear_Algebra.thy Thu Aug 18 23:43:22 2011 +0200
2.2 +++ b/src/HOL/Multivariate_Analysis/Linear_Algebra.thy Thu Aug 18 17:32:02 2011 -0700
2.3 @@ -1756,7 +1756,7 @@
2.4 have Kp: "?K > 0" by arith
2.5 { assume C: "B < 0"
2.6 have "((\<chi>\<chi> i. 1)::'a) \<noteq> 0" unfolding euclidean_eq[where 'a='a]
2.7 - by(auto intro!:exI[where x=0] simp add:euclidean_component_zero)
2.8 + by(auto intro!:exI[where x=0])
2.9 hence "norm ((\<chi>\<chi> i. 1)::'a) > 0" by auto
2.10 with C have "B * norm ((\<chi>\<chi> i. 1)::'a) < 0"
2.11 by (simp add: mult_less_0_iff)
3.1 --- a/src/HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy Thu Aug 18 23:43:22 2011 +0200
3.2 +++ b/src/HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy Thu Aug 18 17:32:02 2011 -0700
3.3 @@ -5570,9 +5570,6 @@
3.4
3.5 subsection {* Some properties of a canonical subspace *}
3.6
3.7 -(** move **)
3.8 -declare euclidean_component_zero[simp]
3.9 -
3.10 lemma subspace_substandard:
3.11 "subspace {x::'a::euclidean_space. (\<forall>i<DIM('a). P i \<longrightarrow> x$$i = 0)}"
3.12 unfolding subspace_def by(auto simp add: euclidean_simps) (* FIXME: duplicate rewrite rule *)