src/ZF/Univ.thy
author lcp
Fri, 16 Dec 1994 17:32:14 +0100
changeset 796 357a1f2dd07e
parent 753 ec86863e87c8
child 1155 928a16e02f9f
permissions -rw-r--r--
now also depends upon Finite.thy

(*  Title: 	ZF/univ.thy
    ID:         $Id$
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1992  University of Cambridge

The cumulative hierarchy and a small universe for recursive types

Standard notation for Vset(i) is V(i), but users might want V for a variable

NOTE: univ(A) could be a translation; would simplify many proofs!
  But Ind_Syntax.univ refers to the constant "univ"
*)

Univ = Arith + Sum + Finite + "mono" +
consts
    Vfrom       :: "[i,i]=>i"
    Vset        :: "i=>i"
    Vrec        :: "[i, [i,i]=>i] =>i"
    univ        :: "i=>i"

translations
    "Vset(x)"   == 	"Vfrom(0,x)"

defs
    Vfrom_def   "Vfrom(A,i) == transrec(i, %x f. A Un (UN y:x. Pow(f`y)))"

    Vrec_def
   	"Vrec(a,H) == transrec(rank(a), %x g. lam z: Vset(succ(x)).      \
\                             H(z, lam w:Vset(x). g`rank(w)`w)) ` a"

    univ_def    "univ(A) == Vfrom(A,nat)"

end