src/ZF/Univ.thy
author clasohm
Tue Feb 06 12:27:17 1996 +0100 (1996-02-06)
changeset 1478 2b8c2a7547ab
parent 1401 0c439768f45c
child 2469 b50b8c0eec01
permissions -rw-r--r--
expanded tabs
     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 NOTE: univ(A) could be a translation; would simplify many proofs!
    11   But Ind_Syntax.univ refers to the constant "univ"
    12 *)
    13 
    14 Univ = Arith + Sum + Finite + "mono" +
    15 consts
    16     Vfrom       :: [i,i]=>i
    17     Vset        :: i=>i
    18     Vrec        :: [i, [i,i]=>i] =>i
    19     univ        :: i=>i
    20 
    21 translations
    22     "Vset(x)"   ==      "Vfrom(0,x)"
    23 
    24 defs
    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