src/HOL/WF_Rel.thy
author paulson
Mon Dec 07 18:26:25 1998 +0100 (1998-12-07)
changeset 6019 0e55c2fb2ebb
parent 3296 2ee6c397003d
child 8262 08ad0a986db2
permissions -rw-r--r--
tidying
     1 (*  Title:      HOL/WF_Rel
     2     ID:         $Id$
     3     Author:     Konrad Slind
     4     Copyright   1995 TU Munich
     5 
     6 Derived WF relations: inverse image, lexicographic product, measure, ...
     7 
     8 The simple relational product, in which (x',y')<(x,y) iff x'<x and y'<y, is a
     9 subset of the lexicographic product, and therefore does not need to be defined
    10 separately.
    11 *)
    12 
    13 WF_Rel = Finite +
    14 consts
    15   less_than :: "(nat*nat)set"
    16   inv_image :: "('b * 'b)set => ('a => 'b) => ('a * 'a)set"
    17   measure   :: "('a => nat) => ('a * 'a)set"
    18   "**"      :: "[('a*'a)set, ('b*'b)set] => (('a*'b)*('a*'b))set" (infixl 70)
    19   finite_psubset  :: "('a set * 'a set) set"
    20 
    21 
    22 defs
    23   less_than_def "less_than == trancl pred_nat"
    24 
    25   inv_image_def "inv_image r f == {(x,y). (f(x), f(y)) : r}"
    26 
    27   measure_def   "measure == inv_image less_than"
    28 
    29   lex_prod_def  "ra**rb == {p. ? a a' b b'. 
    30                                 p = ((a,b),(a',b')) & 
    31                                ((a,a') : ra | a=a' & (b,b') : rb)}"
    32 
    33   (* finite proper subset*)
    34   finite_psubset_def "finite_psubset == {(A,B). A < B & finite B}"
    35 end