src/ZF/OrdQuant.thy
author wenzelm
Fri Nov 09 00:09:47 2001 +0100 (2001-11-09)
changeset 12114 a8e860c86252
parent 6093 87bf8c03b169
child 12552 d2d2ab3f1f37
permissions -rw-r--r--
eliminated old "symbols" syntax, use "xsymbols" instead;
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(*  Title:      ZF/AC/OrdQuant.thy
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    ID:         $Id$
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    Authors:    Krzysztof Grabczewski and L C Paulson
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Quantifiers and union operator for ordinals. 
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*)
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OrdQuant = Ordinal +
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consts
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  (* Ordinal Quantifiers *)
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  oall, oex   :: [i, i => o] => o
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  (* Ordinal Union *)
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  OUnion      :: [i, i => i] => i
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syntax
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  "@oall"     :: [idt, i, o] => o        ("(3ALL _<_./ _)" 10)
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  "@oex"      :: [idt, i, o] => o        ("(3EX _<_./ _)" 10)
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  "@OUNION"   :: [idt, i, i] => i        ("(3UN _<_./ _)" 10)
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translations
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  "ALL x<a. P"  == "oall(a, %x. P)"
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  "EX x<a. P"   == "oex(a, %x. P)"
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  "UN x<a. B"   == "OUnion(a, %x. B)"
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syntax (xsymbols)
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  "@oall"     :: [idt, i, o] => o        ("(3\\<forall> _<_./ _)" 10)
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  "@oex"      :: [idt, i, o] => o        ("(3\\<exists> _<_./ _)" 10)
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  "@OUNION"   :: [idt, i, i] => i        ("(3\\<Union> _<_./ _)" 10)
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defs
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  (* Ordinal Quantifiers *)
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  oall_def      "oall(A, P) == ALL x. x<A --> P(x)"
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  oex_def       "oex(A, P) == EX x. x<A & P(x)"
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  OUnion_def     "OUnion(i,B) == {z: UN x:i. B(x). Ord(i)}"
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end