src/ZF/Nat.thy
author clasohm
Thu Sep 16 12:20:38 1993 +0200 (1993-09-16)
changeset 0 a5a9c433f639
child 6 8ce8c4d13d4d
permissions -rw-r--r--
Initial revision
     1 (*  Title: 	ZF/nat.thy
     2     ID:         $Id$
     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1992  University of Cambridge
     5 
     6 Natural numbers in Zermelo-Fraenkel Set Theory 
     7 *)
     8 
     9 Nat = Ord + Bool + 
    10 consts
    11     nat 	::      "i"
    12     nat_case    ::      "[i, i, i=>i]=>i"
    13     nat_rec     ::      "[i, i, [i,i]=>i]=>i"
    14 
    15 rules
    16 
    17     nat_def     "nat == lfp(Inf, %X. {0} Un {succ(i). i:X})"
    18 
    19     nat_case_def
    20 	"nat_case(k,a,b) == THE y. k=0 & y=a | (EX x. k=succ(x) & y=b(x))"
    21 
    22     nat_rec_def
    23 	"nat_rec(k,a,b) ==   \
    24 \   	  wfrec(Memrel(nat), k, %n f. nat_case(n, a, %m. b(m, f`m)))"
    25 
    26 end