--- a/src/HOL/WF.ML Tue Aug 18 10:24:09 1998 +0200
+++ b/src/HOL/WF.ML Tue Aug 18 10:24:54 1998 +0200
@@ -136,6 +136,21 @@
* Wellfoundedness of `disjoint union'
*---------------------------------------------------------------------------*)
+(*Intuition behind this proof for the case of binary union:
+
+ Goal: find an (R u S)-min element of a nonempty subset A.
+ by case distinction:
+ 1. There is a step a -R-> b with a,b : A.
+ Pick an R-min element z of the (nonempty) set {a:A | EX b:A. a -R-> b}.
+ By definition, there is z':A s.t. z -R-> z'. Because z is R-min in the
+ subset, z' must be R-min in A. Because z' has an R-predecessor, it cannot
+ have an S-successor and is thus S-min in A as well.
+ 2. There is no such step.
+ Pick an S-min element of A. In this case it must be an R-min
+ element of A as well.
+
+*)
+
Goal "[| !i:I. wf(r i); \
\ !i:I.!j:I. r i ~= r j --> Domain(r i) Int Range(r j) = {} & \
\ Domain(r j) Int Range(r i) = {} \