src/ZF/Univ.thy
changeset 0 a5a9c433f639
child 28 b429d6a658ae
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/ZF/Univ.thy	Thu Sep 16 12:20:38 1993 +0200
     1.3 @@ -0,0 +1,34 @@
     1.4 +(*  Title: 	ZF/univ.thy
     1.5 +    ID:         $Id$
     1.6 +    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     1.7 +    Copyright   1992  University of Cambridge
     1.8 +
     1.9 +The cumulative hierarchy and a small universe for recursive types
    1.10 +
    1.11 +Standard notation for Vset(i) is V(i), but users might want V for a variable
    1.12 +*)
    1.13 +
    1.14 +Univ = Arith + Sum +
    1.15 +consts
    1.16 +    Limit       ::      "i=>o"
    1.17 +    Vfrom       ::      "[i,i]=>i"
    1.18 +    Vset        ::      "i=>i"
    1.19 +    Vrec        ::      "[i, [i,i]=>i] =>i"
    1.20 +    univ        ::      "i=>i"
    1.21 +
    1.22 +translations
    1.23 +  (*Apparently a bug prevents using "Vset" == "Vfrom(0)" *)
    1.24 +    "Vset(x)"   == 	"Vfrom(0,x)"
    1.25 +
    1.26 +rules
    1.27 +    Limit_def   "Limit(i) == Ord(i) & 0:i & (ALL y:i. succ(y): i)"
    1.28 +
    1.29 +    Vfrom_def   "Vfrom(A,i) == transrec(i, %x f. A Un (UN y:x. Pow(f`y)))"
    1.30 +
    1.31 +    Vrec_def
    1.32 +   	"Vrec(a,H) == transrec(rank(a), %x g. lam z: Vset(succ(x)).      \
    1.33 +\                             H(z, lam w:Vset(x). g`rank(w)`w)) ` a"
    1.34 +
    1.35 +    univ_def    "univ(A) == Vfrom(A,nat)"
    1.36 +
    1.37 +end