--- a/src/HOL/Multivariate_Analysis/Euclidean_Space.thy Mon Aug 15 14:29:17 2011 -0700
+++ b/src/HOL/Multivariate_Analysis/Euclidean_Space.thy Mon Aug 15 14:50:24 2011 -0700
@@ -272,9 +272,6 @@
subsubsection {* Type @{typ "'a \<times> 'b"} *}
-lemma disjoint_iff: "A \<inter> B = {} \<longleftrightarrow> (\<forall>x\<in>A. \<forall>y\<in>B. x \<noteq> y)"
- by auto (* TODO: move elsewhere *)
-
instantiation prod :: (euclidean_space, euclidean_space) euclidean_space
begin
@@ -307,7 +304,7 @@
next
show "DIM('a \<times> 'b) = card (Basis :: ('a \<times> 'b) set)"
unfolding dimension_prod_def Basis_prod_def
- by (simp add: card_Un_disjoint disjoint_iff
+ by (simp add: card_Un_disjoint disjoint_iff_not_equal
card_image inj_on_def dimension_def)
next
show "basis ` {..<DIM('a \<times> 'b)} = (Basis :: ('a \<times> 'b) set)"