src/HOL/Library/Product_Vector.thy
 changeset 44066 d74182c93f04 parent 37678 0040bafffdef child 44126 ce44e70d0c47
```--- a/src/HOL/Library/Product_Vector.thy	Mon Aug 08 10:26:26 2011 -0700
+++ b/src/HOL/Library/Product_Vector.thy	Mon Aug 08 10:32:55 2011 -0700
@@ -28,13 +28,13 @@
instance proof
fix a b :: real and x y :: "'a \<times> 'b"
show "scaleR a (x + y) = scaleR a x + scaleR a y"
-    by (simp add: expand_prod_eq scaleR_right_distrib)
+    by (simp add: prod_eq_iff scaleR_right_distrib)
show "scaleR (a + b) x = scaleR a x + scaleR b x"
-    by (simp add: expand_prod_eq scaleR_left_distrib)
+    by (simp add: prod_eq_iff scaleR_left_distrib)
show "scaleR a (scaleR b x) = scaleR (a * b) x"
show "scaleR 1 x = x"
qed

end
@@ -174,7 +174,7 @@
instance proof
fix x y :: "'a \<times> 'b"
show "dist x y = 0 \<longleftrightarrow> x = y"
-    unfolding dist_prod_def expand_prod_eq by simp
+    unfolding dist_prod_def prod_eq_iff by simp
next
fix x y z :: "'a \<times> 'b"
show "dist x y \<le> dist x z + dist y z"
@@ -373,7 +373,7 @@
unfolding norm_prod_def by simp
show "norm x = 0 \<longleftrightarrow> x = 0"
unfolding norm_prod_def