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