src/HOL/Hoare/Arith2.thy
author clasohm
Wed, 29 Nov 1995 17:01:41 +0100
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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