src/HOL/Wellfounded_Relations.thy
author wenzelm
Thu Dec 06 00:40:04 2001 +0100 (2001-12-06)
changeset 12398 9c27f28c8f5a
parent 11454 7514e5e21cb8
child 15346 ac272926fb77
permissions -rw-r--r--
renamed Finite to Finite_Set;
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(*  Title:      HOL/Wellfounded_Relations
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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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Wellfounded_Relations = Finite_Set + 
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constdefs
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 less_than :: "(nat*nat)set"
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"less_than == trancl pred_nat"
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 measure   :: "('a => nat) => ('a * 'a)set"
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"measure == inv_image less_than"
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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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"ra <*lex*> rb == {((a,b),(a',b')). (a,a') : ra | a=a' & (b,b') : rb}"
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 (* finite proper subset*)
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 finite_psubset  :: "('a set * 'a set) set"
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"finite_psubset == {(A,B). A < B & finite B}"
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(* For rec_defs where the first n parameters stay unchanged in the recursive
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   call. See Library/While_Combinator.thy for an application.
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*)
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 same_fst :: "('a => bool) => ('a => ('b * 'b)set) => (('a*'b)*('a*'b))set"
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"same_fst P R == {((x',y'),(x,y)) . x'=x & P x & (y',y) : R x}"
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end