src/ZF/Univ.thy
 author clasohm Thu Sep 16 12:20:38 1993 +0200 (1993-09-16) changeset 0 a5a9c433f639 child 28 b429d6a658ae permissions -rw-r--r--
Initial revision
```     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
```
```     9 *)
```
```    10
```
```    11 Univ = Arith + Sum +
```
```    12 consts
```
```    13     Limit       ::      "i=>o"
```
```    14     Vfrom       ::      "[i,i]=>i"
```
```    15     Vset        ::      "i=>i"
```
```    16     Vrec        ::      "[i, [i,i]=>i] =>i"
```
```    17     univ        ::      "i=>i"
```
```    18
```
```    19 translations
```
```    20   (*Apparently a bug prevents using "Vset" == "Vfrom(0)" *)
```
```    21     "Vset(x)"   == 	"Vfrom(0,x)"
```
```    22
```
```    23 rules
```
```    24     Limit_def   "Limit(i) == Ord(i) & 0:i & (ALL y:i. succ(y): i)"
```
```    25
```
```    26     Vfrom_def   "Vfrom(A,i) == transrec(i, %x f. A Un (UN y:x. Pow(f`y)))"
```
```    27
```
```    28     Vrec_def
```
```    29    	"Vrec(a,H) == transrec(rank(a), %x g. lam z: Vset(succ(x)).      \
```
```    30 \                             H(z, lam w:Vset(x). g`rank(w)`w)) ` a"
```
```    31
```
```    32     univ_def    "univ(A) == Vfrom(A,nat)"
```
```    33
```
```    34 end
```