|
0
|
1 |
(* Title: ZF/univ.thy
|
|
|
2 |
ID: $Id$
|
|
|
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
|
|
|
4 |
Copyright 1992 University of Cambridge
|
|
|
5 |
|
|
|
6 |
The cumulative hierarchy and a small universe for recursive types
|
|
|
7 |
|
|
|
8 |
Standard notation for Vset(i) is V(i), but users might want V for a variable
|
|
516
|
9 |
|
|
|
10 |
NOTE: univ(A) could be a translation; would simplify many proofs!
|
|
|
11 |
But Ind_Syntax.univ refers to the constant "univ"
|
|
0
|
12 |
*)
|
|
|
13 |
|
|
516
|
14 |
Univ = Arith + Sum + "mono" +
|
|
0
|
15 |
consts
|
|
435
|
16 |
Vfrom :: "[i,i]=>i"
|
|
|
17 |
Vset :: "i=>i"
|
|
|
18 |
Vrec :: "[i, [i,i]=>i] =>i"
|
|
|
19 |
univ :: "i=>i"
|
|
0
|
20 |
|
|
|
21 |
translations
|
|
|
22 |
"Vset(x)" == "Vfrom(0,x)"
|
|
|
23 |
|
|
|
24 |
rules
|
|
|
25 |
Vfrom_def "Vfrom(A,i) == transrec(i, %x f. A Un (UN y:x. Pow(f`y)))"
|
|
|
26 |
|
|
|
27 |
Vrec_def
|
|
|
28 |
"Vrec(a,H) == transrec(rank(a), %x g. lam z: Vset(succ(x)). \
|
|
|
29 |
\ H(z, lam w:Vset(x). g`rank(w)`w)) ` a"
|
|
|
30 |
|
|
|
31 |
univ_def "univ(A) == Vfrom(A,nat)"
|
|
|
32 |
|
|
|
33 |
end
|