(* Title: ZF/nat.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1992 University of Cambridge
Natural numbers in Zermelo-Fraenkel Set Theory
*)
Nat = Ord + Bool + "mono" +
consts
nat :: "i"
nat_case :: "[i, i=>i, i]=>i"
nat_rec :: "[i, i, [i,i]=>i]=>i"
rules
nat_def "nat == lfp(Inf, %X. {0} Un {succ(i). i:X})"
nat_case_def
"nat_case(a,b,k) == THE y. k=0 & y=a | (EX x. k=succ(x) & y=b(x))"
nat_rec_def
"nat_rec(k,a,b) == \
\ wfrec(Memrel(nat), k, %n f. nat_case(a, %m. b(m, f`m), n))"
end