src/ZF/Univ.thy
 author wenzelm Tue Jan 12 15:17:37 1999 +0100 (1999-01-12 ago) changeset 6093 87bf8c03b169 parent 6053 8a1059aa01f0 child 9395 1c9851cdfe9f permissions -rw-r--r--
eliminated global/local names;
```     1 (*  Title:      ZF/univ.thy
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```     2     ID:         \$Id\$
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```     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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```     4     Copyright   1992  University of Cambridge
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```     5
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```     6 The cumulative hierarchy and a small universe for recursive types
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```     7
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```     8 Standard notation for Vset(i) is V(i), but users might want V for a variable
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```     9
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```    10 NOTE: univ(A) could be a translation; would simplify many proofs!
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```    11   But Ind_Syntax.univ refers to the constant "Univ.univ"
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```    12 *)
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```    13
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```    14 Univ = Arith + Sum + Finite + mono +
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```    15
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```    16 consts
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```    17     Vfrom       :: [i,i]=>i
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```    18     Vset        :: i=>i
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```    19     Vrec        :: [i, [i,i]=>i] =>i
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```    20     Vrecursor   :: [[i,i]=>i, i] =>i
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```    21     univ        :: i=>i
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```    22
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```    23 translations
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```    24     "Vset(x)"   ==      "Vfrom(0,x)"
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```    25
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```    26
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```    27 defs
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```    28     Vfrom_def   "Vfrom(A,i) == transrec(i, %x f. A Un (UN y:x. Pow(f`y)))"
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```    29
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```    30     Vrec_def
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```    31         "Vrec(a,H) == transrec(rank(a), %x g. lam z: Vset(succ(x)).
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```    32                              H(z, lam w:Vset(x). g`rank(w)`w)) ` a"
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```    33
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```    34     Vrecursor_def
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```    35         "Vrecursor(H,a) == transrec(rank(a), %x g. lam z: Vset(succ(x)).
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```    36                                     H(lam w:Vset(x). g`rank(w)`w, z)) ` a"
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```    37
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```    38     univ_def    "univ(A) == Vfrom(A,nat)"
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```    39
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```    40 end
```