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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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NOTE: univ(A) could be a translation; would simplify many proofs!


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But Ind_Syntax.univ refers to the constant "univ"

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*)


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Univ = Arith + Sum + Finite + "mono" +

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consts

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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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"Vset(x)" == "Vfrom(0,x)"


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defs

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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
