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
clasohm@0
     1
(*  Title: 	ZF/univ.thy
clasohm@0
     2
    ID:         $Id$
clasohm@0
     3
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0
     4
    Copyright   1992  University of Cambridge
clasohm@0
     5
clasohm@0
     6
The cumulative hierarchy and a small universe for recursive types
clasohm@0
     7
clasohm@0
     8
Standard notation for Vset(i) is V(i), but users might want V for a variable
clasohm@0
     9
*)
clasohm@0
    10
clasohm@0
    11
Univ = Arith + Sum +
clasohm@0
    12
consts
clasohm@0
    13
    Limit       ::      "i=>o"
clasohm@0
    14
    Vfrom       ::      "[i,i]=>i"
clasohm@0
    15
    Vset        ::      "i=>i"
clasohm@0
    16
    Vrec        ::      "[i, [i,i]=>i] =>i"
clasohm@0
    17
    univ        ::      "i=>i"
clasohm@0
    18
clasohm@0
    19
translations
clasohm@0
    20
  (*Apparently a bug prevents using "Vset" == "Vfrom(0)" *)
clasohm@0
    21
    "Vset(x)"   == 	"Vfrom(0,x)"
clasohm@0
    22
clasohm@0
    23
rules
clasohm@0
    24
    Limit_def   "Limit(i) == Ord(i) & 0:i & (ALL y:i. succ(y): i)"
clasohm@0
    25
clasohm@0
    26
    Vfrom_def   "Vfrom(A,i) == transrec(i, %x f. A Un (UN y:x. Pow(f`y)))"
clasohm@0
    27
clasohm@0
    28
    Vrec_def
clasohm@0
    29
   	"Vrec(a,H) == transrec(rank(a), %x g. lam z: Vset(succ(x)).      \
clasohm@0
    30
\                             H(z, lam w:Vset(x). g`rank(w)`w)) ` a"
clasohm@0
    31
clasohm@0
    32
    univ_def    "univ(A) == Vfrom(A,nat)"
clasohm@0
    33
clasohm@0
    34
end