src/ZF/Univ.thy

+(*  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