(* 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