|
1478
|
1 |
(* Title: ZF/Nat.thy
|
|
0
|
2 |
ID: $Id$
|
|
1478
|
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
|
|
435
|
4 |
Copyright 1994 University of Cambridge
|
|
0
|
5 |
|
|
|
6 |
Natural numbers in Zermelo-Fraenkel Set Theory
|
|
|
7 |
*)
|
|
|
8 |
|
|
2469
|
9 |
Nat = OrdQuant + Bool + mono +
|
|
0
|
10 |
consts
|
|
1478
|
11 |
nat :: i
|
|
1401
|
12 |
nat_case :: [i, i=>i, i]=>i
|
|
|
13 |
nat_rec :: [i, i, [i,i]=>i]=>i
|
|
0
|
14 |
|
|
753
|
15 |
defs
|
|
0
|
16 |
|
|
|
17 |
nat_def "nat == lfp(Inf, %X. {0} Un {succ(i). i:X})"
|
|
|
18 |
|
|
|
19 |
nat_case_def
|
|
1478
|
20 |
"nat_case(a,b,k) == THE y. k=0 & y=a | (EX x. k=succ(x) & y=b(x))"
|
|
0
|
21 |
|
|
|
22 |
nat_rec_def
|
|
1478
|
23 |
"nat_rec(k,a,b) ==
|
|
|
24 |
wfrec(Memrel(nat), k, %n f. nat_case(a, %m. b(m, f`m), n))"
|
|
0
|
25 |
|
|
|
26 |
end
|