src/ZF/Rel.thy
author clasohm
Sat Dec 09 13:36:11 1995 +0100 (1995-12-09 ago)
changeset 1401 0c439768f45c
parent 1155 928a16e02f9f
child 1478 2b8c2a7547ab
permissions -rw-r--r--
removed quotes from consts and syntax sections
     1 (*  Title: 	ZF/Rel.thy
     2     ID:         $Id$
     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1994  University of Cambridge
     5 
     6 Relations in Zermelo-Fraenkel Set Theory 
     7 *)
     8 
     9 Rel = ZF +
    10 consts
    11     refl,irrefl,equiv      :: [i,i]=>o
    12     sym,asym,antisym,trans :: i=>o
    13     trans_on               :: [i,i]=>o	("trans[_]'(_')")
    14 
    15 defs
    16   refl_def     "refl(A,r) == (ALL x: A. <x,x> : r)"
    17 
    18   irrefl_def   "irrefl(A,r) == ALL x: A. <x,x> ~: r"
    19 
    20   sym_def      "sym(r) == ALL x y. <x,y>: r --> <y,x>: r"
    21 
    22   asym_def     "asym(r) == ALL x y. <x,y>:r --> ~ <y,x>:r"
    23 
    24   antisym_def  "antisym(r) == ALL x y.<x,y>:r --> <y,x>:r --> x=y"
    25 
    26   trans_def    "trans(r) == ALL x y z. <x,y>: r --> <y,z>: r --> <x,z>: r"
    27 
    28   trans_on_def "trans[A](r) == ALL x:A. ALL y:A. ALL z:A. 	
    29                           <x,y>: r --> <y,z>: r --> <x,z>: r"
    30 
    31   equiv_def    "equiv(A,r) == r <= A*A & refl(A,r) & sym(r) & trans(r)"
    32 
    33 end