src/ZF/Univ.thy
author wenzelm
Tue Jan 12 15:17:37 1999 +0100 (1999-01-12 ago)
changeset 6093 87bf8c03b169
parent 6053 8a1059aa01f0
child 9395 1c9851cdfe9f
permissions -rw-r--r--
eliminated global/local names;
     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.univ"
    12 *)
    13 
    14 Univ = Arith + Sum + Finite + mono +
    15 
    16 consts
    17     Vfrom       :: [i,i]=>i
    18     Vset        :: i=>i
    19     Vrec        :: [i, [i,i]=>i] =>i
    20     Vrecursor   :: [[i,i]=>i, i] =>i
    21     univ        :: i=>i
    22 
    23 translations
    24     "Vset(x)"   ==      "Vfrom(0,x)"
    25 
    26 
    27 defs
    28     Vfrom_def   "Vfrom(A,i) == transrec(i, %x f. A Un (UN y:x. Pow(f`y)))"
    29 
    30     Vrec_def
    31         "Vrec(a,H) == transrec(rank(a), %x g. lam z: Vset(succ(x)).      
    32                              H(z, lam w:Vset(x). g`rank(w)`w)) ` a"
    33 
    34     Vrecursor_def
    35         "Vrecursor(H,a) == transrec(rank(a), %x g. lam z: Vset(succ(x)).      
    36                                     H(lam w:Vset(x). g`rank(w)`w, z)) ` a"
    37 
    38     univ_def    "univ(A) == Vfrom(A,nat)"
    39 
    40 end