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