src/ZF/Nat.thy
changeset 0 a5a9c433f639
child 6 8ce8c4d13d4d
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/ZF/Nat.thy	Thu Sep 16 12:20:38 1993 +0200
     1.3 @@ -0,0 +1,26 @@
     1.4 +(*  Title: 	ZF/nat.thy
     1.5 +    ID:         $Id$
     1.6 +    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     1.7 +    Copyright   1992  University of Cambridge
     1.8 +
     1.9 +Natural numbers in Zermelo-Fraenkel Set Theory 
    1.10 +*)
    1.11 +
    1.12 +Nat = Ord + Bool + 
    1.13 +consts
    1.14 +    nat 	::      "i"
    1.15 +    nat_case    ::      "[i, i, i=>i]=>i"
    1.16 +    nat_rec     ::      "[i, i, [i,i]=>i]=>i"
    1.17 +
    1.18 +rules
    1.19 +
    1.20 +    nat_def     "nat == lfp(Inf, %X. {0} Un {succ(i). i:X})"
    1.21 +
    1.22 +    nat_case_def
    1.23 +	"nat_case(k,a,b) == THE y. k=0 & y=a | (EX x. k=succ(x) & y=b(x))"
    1.24 +
    1.25 +    nat_rec_def
    1.26 +	"nat_rec(k,a,b) ==   \
    1.27 +\   	  wfrec(Memrel(nat), k, %n f. nat_case(n, a, %m. b(m, f`m)))"
    1.28 +
    1.29 +end