src/ZF/Univ.thy
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Thu, 16 Sep 1993 12:20:38 +0200
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(*  Title: 	ZF/univ.thy
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    ID:         $Id$
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    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1992  University of Cambridge
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The cumulative hierarchy and a small universe for recursive types
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Standard notation for Vset(i) is V(i), but users might want V for a variable
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*)
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Univ = Arith + Sum +
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consts
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    Limit       ::      "i=>o"
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    Vfrom       ::      "[i,i]=>i"
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    Vset        ::      "i=>i"
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    Vrec        ::      "[i, [i,i]=>i] =>i"
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    univ        ::      "i=>i"
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translations
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  (*Apparently a bug prevents using "Vset" == "Vfrom(0)" *)
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    "Vset(x)"   == 	"Vfrom(0,x)"
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rules
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    Limit_def   "Limit(i) == Ord(i) & 0:i & (ALL y:i. succ(y): i)"
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    Vfrom_def   "Vfrom(A,i) == transrec(i, %x f. A Un (UN y:x. Pow(f`y)))"
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    Vrec_def
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   	"Vrec(a,H) == transrec(rank(a), %x g. lam z: Vset(succ(x)).      \
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\                             H(z, lam w:Vset(x). g`rank(w)`w)) ` a"
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    univ_def    "univ(A) == Vfrom(A,nat)"
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end