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(* Title : NSCA.thy
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Author : Jacques D. Fleuriot
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Copyright : 2001,2002 University of Edinburgh
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Description : Infinite, infinitesimal complex number etc!
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*)
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14320
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NSCA = NSComplexArith +
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13957
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consts
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(* infinitely close *)
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"@c=" :: [hcomplex,hcomplex] => bool (infixl 50)
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constdefs
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(* standard complex numbers reagarded as an embedded subset of NS complex *)
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SComplex :: "hcomplex set"
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"SComplex == {x. EX r. x = hcomplex_of_complex r}"
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CInfinitesimal :: "hcomplex set"
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"CInfinitesimal == {x. ALL r: Reals. 0 < r --> hcmod x < r}"
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CFinite :: "hcomplex set"
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"CFinite == {x. EX r: Reals. hcmod x < r}"
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CInfinite :: "hcomplex set"
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"CInfinite == {x. ALL r: Reals. r < hcmod x}"
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(* standard part map *)
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stc :: hcomplex => hcomplex
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"stc x == (@r. x : CFinite & r:SComplex & r @c= x)"
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cmonad :: hcomplex => hcomplex set
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"cmonad x == {y. x @c= y}"
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cgalaxy :: hcomplex => hcomplex set
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"cgalaxy x == {y. (x - y) : CFinite}"
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defs
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capprox_def "x @c= y == (x - y) : CInfinitesimal"
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end
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