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src/HOL/WF.ML

changeset 5330 | 8c9fadda81f4 |

parent 5318 | 72bf8039b53f |

child 5337 | 2f7d09a927c4 |

--- 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) = {} \