src/ZF/Univ.thy
 author wenzelm Tue, 12 Jan 1999 15:17:37 +0100 changeset 6093 87bf8c03b169 parent 6053 8a1059aa01f0 child 9395 1c9851cdfe9f permissions -rw-r--r--
eliminated global/local names;
```
(*  Title:      ZF/univ.thy
ID:         \$Id\$
Author:     Lawrence C Paulson, Cambridge University Computer Laboratory

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"
*)

Univ = Arith + Sum + Finite + mono +

consts
Vfrom       :: [i,i]=>i
Vset        :: i=>i
Vrec        :: [i, [i,i]=>i] =>i
Vrecursor   :: [[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"

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

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

end
```