author | wenzelm |
Tue, 25 Jul 2000 00:06:46 +0200 | |
changeset 9436 | 62bb04ab4b01 |
parent 9361 | 8b09c29453ac |
child 9443 | 3c2fc90d4e8a |
permissions | -rw-r--r-- |
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(* Title: HOL/WF_Rel |
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ID: $Id$ |
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Author: Konrad Slind |
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Copyright 1995 TU Munich |
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Derived WF relations: inverse image, lexicographic product, measure, ... |
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The simple relational product, in which (x',y')<(x,y) iff x'<x and y'<y, is a |
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subset of the lexicographic product, and therefore does not need to be defined |
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separately. |
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*) |
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Distributed Psubset stuff to basic set theory files, incl Finite.
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WF_Rel = Finite + |
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(* actually belongs to Finite.thy *) |
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instance unit :: finite (finite_unit) |
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instance "*" :: (finite,finite) finite (finite_Prod) |
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consts |
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less_than :: "(nat*nat)set" |
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inv_image :: "('b * 'b)set => ('a => 'b) => ('a * 'a)set" |
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measure :: "('a => nat) => ('a * 'a)set" |
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lex_prod :: "[('a*'a)set, ('b*'b)set] => (('a*'b)*('a*'b))set" |
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(infixr "<*lex*>" 80) |
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finite_psubset :: "('a set * 'a set) set" |
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defs |
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less_than_def "less_than == trancl pred_nat" |
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inv_image_def "inv_image r f == {(x,y). (f(x), f(y)) : r}" |
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Relation "less_than" internalizes "<" for easy use of TFL
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measure_def "measure == inv_image less_than" |
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lex_prod_def "ra <*lex*> rb == {((a,b),(a',b')) | a a' b b'. |
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((a,a') : ra | a=a' & (b,b') : rb)}" |
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(* finite proper subset*) |
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finite_psubset_def "finite_psubset == {(A,B). A < B & finite B}" |
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end |