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(* Title: HOL/Hoare/Arith2.thy
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ID: $Id$
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Author: Norbert Galm
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Copyright 1995 TUM
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More arithmetic.
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*)
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Arith2 = Arith +
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consts
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divides :: [nat, nat] => bool (infixl 70)
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cd :: [nat, nat, nat] => bool
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gcd :: [nat, nat] => nat
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pow :: [nat, nat] => nat (infixl 75)
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fac :: nat => nat
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defs
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divides_def "x divides n == 0<n & 0<x & (n mod x) = 0"
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cd_def "cd x m n == x divides m & x divides n"
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gcd_def "gcd m n == @x.(cd x m n) & (!y.(cd y m n) --> y<=x)"
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pow_def "m pow n == nat_rec n (Suc 0) (%u v.m*v)"
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fac_def "fac m == nat_rec m (Suc 0) (%u v.(Suc u)*v)"
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end
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