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;
     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_Set + 
    14 
    15 constdefs
    16  less_than :: "(nat*nat)set"
    17 "less_than == trancl pred_nat"
    18 
    19  measure   :: "('a => nat) => ('a * 'a)set"
    20 "measure == inv_image less_than"
    21 
    22  lex_prod  :: "[('a*'a)set, ('b*'b)set] => (('a*'b)*('a*'b))set"
    23                (infixr "<*lex*>" 80)
    24 "ra <*lex*> rb == {((a,b),(a',b')). (a,a') : ra | a=a' & (b,b') : rb}"
    25 
    26  (* finite proper subset*)
    27  finite_psubset  :: "('a set * 'a set) set"
    28 "finite_psubset == {(A,B). A < B & finite B}"
    29 
    30 (* For rec_defs where the first n parameters stay unchanged in the recursive
    31    call. See Library/While_Combinator.thy for an application.
    32 *)
    33  same_fst :: "('a => bool) => ('a => ('b * 'b)set) => (('a*'b)*('a*'b))set"
    34 "same_fst P R == {((x',y'),(x,y)) . x'=x & P x & (y',y) : R x}"
    35 
    36 end