src/ZF/Univ.thy
 author clasohm Tue Feb 06 12:27:17 1996 +0100 (1996-02-06) changeset 1478 2b8c2a7547ab parent 1401 0c439768f45c child 2469 b50b8c0eec01 permissions -rw-r--r--
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1 (*  Title:      ZF/univ.thy
2     ID:         \$Id\$
3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
4     Copyright   1992  University of Cambridge
6 The cumulative hierarchy and a small universe for recursive types
8 Standard notation for Vset(i) is V(i), but users might want V for a variable
10 NOTE: univ(A) could be a translation; would simplify many proofs!
11   But Ind_Syntax.univ refers to the constant "univ"
12 *)
14 Univ = Arith + Sum + Finite + "mono" +
15 consts
16     Vfrom       :: [i,i]=>i
17     Vset        :: i=>i
18     Vrec        :: [i, [i,i]=>i] =>i
19     univ        :: i=>i
21 translations
22     "Vset(x)"   ==      "Vfrom(0,x)"
24 defs
25     Vfrom_def   "Vfrom(A,i) == transrec(i, %x f. A Un (UN y:x. Pow(f`y)))"
27     Vrec_def
28         "Vrec(a,H) == transrec(rank(a), %x g. lam z: Vset(succ(x)).
29                              H(z, lam w:Vset(x). g`rank(w)`w)) ` a"
31     univ_def    "univ(A) == Vfrom(A,nat)"
33 end