1.1 --- a/src/HOL/WF.ML Tue Aug 18 10:24:09 1998 +0200
1.2 +++ b/src/HOL/WF.ML Tue Aug 18 10:24:54 1998 +0200
1.3 @@ -136,6 +136,21 @@
1.4 * Wellfoundedness of `disjoint union'
1.5 *---------------------------------------------------------------------------*)
1.6
1.7 +(*Intuition behind this proof for the case of binary union:
1.8 +
1.9 + Goal: find an (R u S)-min element of a nonempty subset A.
1.10 + by case distinction:
1.11 + 1. There is a step a -R-> b with a,b : A.
1.12 + Pick an R-min element z of the (nonempty) set {a:A | EX b:A. a -R-> b}.
1.13 + By definition, there is z':A s.t. z -R-> z'. Because z is R-min in the
1.14 + subset, z' must be R-min in A. Because z' has an R-predecessor, it cannot
1.15 + have an S-successor and is thus S-min in A as well.
1.16 + 2. There is no such step.
1.17 + Pick an S-min element of A. In this case it must be an R-min
1.18 + element of A as well.
1.19 +
1.20 +*)
1.21 +
1.22 Goal "[| !i:I. wf(r i); \
1.23 \ !i:I.!j:I. r i ~= r j --> Domain(r i) Int Range(r j) = {} & \
1.24 \ Domain(r j) Int Range(r i) = {} \