src/HOLCF/Porder.thy
author clasohm
Tue, 06 Feb 1996 12:42:31 +0100
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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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defs
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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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(* 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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rules
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lub             "lub(S) = (@x. S <<| x)"
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(* start 8bit 1 *)
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(* end 8bit 1 *)
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end 
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