src/HOL/Wellfounded_Relations.thy
author nipkow
Thu Oct 12 18:44:35 2000 +0200 (2000-10-12)
changeset 10213 01c2744a3786
child 11008 f7333f055ef6
permissions -rw-r--r--
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     1 (*  Title:      HOL/Wellfounded_Relations
     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 Wellfounded_Relations = Finite +
    14 
    15 (* actually belongs to theory Finite *)
    16 instance unit :: finite                  (finite_unit)
    17 instance "*" :: (finite,finite) finite   (finite_Prod)
    18 
    19 
    20 constdefs
    21  less_than :: "(nat*nat)set"
    22 "less_than == trancl pred_nat"
    23 
    24  inv_image :: "('b * 'b)set => ('a => 'b) => ('a * 'a)set"
    25 "inv_image r f == {(x,y). (f(x), f(y)) : r}"
    26 
    27  measure   :: "('a => nat) => ('a * 'a)set"
    28 "measure == inv_image less_than"
    29 
    30  lex_prod  :: "[('a*'a)set, ('b*'b)set] => (('a*'b)*('a*'b))set"
    31                (infixr "<*lex*>" 80)
    32 "ra <*lex*> rb == {((a,b),(a',b')). (a,a') : ra | a=a' & (b,b') : rb}"
    33 
    34  (* finite proper subset*)
    35  finite_psubset  :: "('a set * 'a set) set"
    36 "finite_psubset == {(A,B). A < B & finite B}"
    37 
    38 (* For rec_defs where the first n parameters stay unchanged in the recursive
    39    call. See While for an application.
    40 *)
    41  same_fst :: "('a => bool) => ('a => ('b * 'b)set) => (('a*'b)*('a*'b))set"
    42 "same_fst P R == {((x',y'),(x,y)) . x'=x & P x & (y',y) : R x}"
    43 
    44 end