src/HOL/Real/RealDef.thy
 changeset 14658 b1293d0f8d5f parent 14497 76cdbeb0c9de child 14691 e1eedc8cad37
```--- a/src/HOL/Real/RealDef.thy	Thu Apr 22 13:26:47 2004 +0200
+++ b/src/HOL/Real/RealDef.thy	Fri Apr 23 11:04:07 2004 +0200
@@ -158,12 +158,12 @@
"Abs_Real (realrel``{(x,y)}) + Abs_Real (realrel``{(u,v)}) =
Abs_Real (realrel``{(x+u, y+v)})"
proof -
-  have "congruent2 realrel
+  have "congruent2 realrel realrel
(\<lambda>z w. (\<lambda>(x,y). (\<lambda>(u,v). {Abs_Real (realrel `` {(x+u, y+v)})}) w) z)"
by (simp add: congruent2_def, blast intro: real_add_congruent2_lemma)
thus ?thesis
-                  UN_equiv_class2 [OF equiv_realrel])
+                  UN_equiv_class2 [OF equiv_realrel equiv_realrel])
qed

lemma real_add_commute: "(z::real) + w = w + z"
@@ -207,10 +207,10 @@
done

lemma real_mult_congruent2:
-    "congruent2 realrel (%p1 p2.
+    "congruent2 realrel realrel (%p1 p2.
(%(x1,y1). (%(x2,y2).
{ Abs_Real (realrel``{(x1*x2 + y1*y2, x1*y2+y1*x2)}) }) p2) p1)"
-apply (rule equiv_realrel [THEN congruent2_commuteI], clarify)
+apply (rule congruent2_commuteI [OF equiv_realrel], clarify)