(* 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
*)
Univ = Arith + Sum +
consts
Limit :: "i=>o"
Vfrom :: "[i,i]=>i"
Vset :: "i=>i"
Vrec :: "[i, [i,i]=>i] =>i"
univ :: "i=>i"
translations
(*Apparently a bug prevents using "Vset" == "Vfrom(0)" *)
"Vset(x)" == "Vfrom(0,x)"
rules
Limit_def "Limit(i) == Ord(i) & 0:i & (ALL y:i. succ(y): i)"
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