src/HOL/Hoare/Arith2.thy
author clasohm
Mon Feb 05 21:29:06 1996 +0100 (1996-02-05)
changeset 1476 608483c2122a
parent 1374 5e407f2a3323
child 1558 9c6ebfab4e05
permissions -rw-r--r--
expanded tabs; incorporated Konrad's changes
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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