Distributed Psubset stuff to basic set theory files, incl Finite.
Added stuff by bu.
(* Title: HOL/WF_Rel
ID: $Id$
Author: Konrad Slind
Copyright 1995 TU Munich
Derived wellfounded relations: inverse image, relational product, measure, ...
*)
WF_Rel = Finite +
consts
inv_image :: "('b * 'b)set => ('a => 'b) => ('a * 'a)set"
measure :: "('a => nat) => ('a * 'a)set"
"**" :: "[('a*'a)set, ('b*'b)set] => (('a*'b)*('a*'b))set" (infixl 70)
rprod :: "[('a*'a)set, ('b*'b)set] => (('a*'b)*('a*'b))set"
finite_psubset :: "('a set * 'a set) set"
defs
inv_image_def "inv_image r f == {(x,y). (f(x), f(y)) : r}"
measure_def "measure == inv_image (trancl pred_nat)"
lex_prod_def "ra**rb == {p. ? a a' b b'.
p = ((a,b),(a',b')) &
((a,a') : ra | a=a' & (b,b') : rb)}"
rprod_def "rprod ra rb == {p. ? a a' b b'.
p = ((a,b),(a',b')) &
((a,a') : ra & (b,b') : rb)}"
(* finite proper subset*)
finite_psubset_def "finite_psubset == {(A,B). A < B & finite B}"
end