| author | wenzelm |
| Wed, 26 Sep 2001 22:24:55 +0200 | |
| changeset 11572 | 93da54c8a687 |
| parent 297 | 5ef75ff3baeb |
| permissions | -rw-r--r-- |
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(* Title: HOLCF/porder.thy |
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ID: $Id$ |
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Author: Franz Regensburger |
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Copyright 1993 Technische Universitaet Muenchen |
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Conservative extension of theory Porder0 by constant definitions |
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*) |
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Porder = Porder0 + |
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consts |
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"<|" :: "['a set,'a::po] => bool" (infixl 55) |
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"<<|" :: "['a set,'a::po] => bool" (infixl 55) |
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lub :: "'a set => 'a::po" |
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is_tord :: "'a::po set => bool" |
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is_chain :: "(nat=>'a::po) => bool" |
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max_in_chain :: "[nat,nat=>'a::po]=>bool" |
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finite_chain :: "(nat=>'a::po)=>bool" |
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rules |
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(* class definitions *) |
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is_ub "S <| x == ! y.y:S --> y<<x" |
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is_lub "S <<| x == S <| x & (! u. S <| u --> x << u)" |
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lub "lub(S) = (@x. S <<| x)" |
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(* Arbitrary chains are total orders *) |
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is_tord "is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)" |
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(* Here we use countable chains and I prefer to code them as functions! *) |
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is_chain "is_chain(F) == (! i.F(i) << F(Suc(i)))" |
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(* finite chains, needed for monotony of continouous functions *) |
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max_in_chain_def "max_in_chain(i,C) == ! j. i <= j --> C(i) = C(j)" |
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finite_chain_def "finite_chain(C) == is_chain(C) & (? i. max_in_chain(i,C))" |
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end |