src/ZF/Univ.thy
 author paulson Fri, 03 Jan 1997 15:01:55 +0100 changeset 2469 b50b8c0eec01 parent 1478 2b8c2a7547ab child 3923 c257b82a1200 permissions -rw-r--r--
Implicit simpsets and clasets for FOL and ZF
```
(*  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 = 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
```