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(* Title: HOL/Divides.thy
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ID: $Id$
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 1993 University of Cambridge
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The division operators div, mod and the divides relation "dvd"
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*)
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Divides = Arith +
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consts
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div, mod :: [nat, nat] => nat (infixl 70)
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dvd :: [nat,nat]=>bool (infixl 70)
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defs
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mod_def "m mod n == wfrec (trancl pred_nat)
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(%f j. if j<n then j else f (j-n)) m"
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div_def "m div n == wfrec (trancl pred_nat)
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(%f j. if j<n then 0 else Suc (f (j-n))) m"
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dvd_def "m dvd n == EX k. n = m*k"
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end
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