src/HOL/Hoare/Arith2.thy
changeset 1335 5e1c0540f285
child 1374 5e407f2a3323
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/HOL/Hoare/Arith2.thy	Fri Nov 17 09:04:10 1995 +0100
     1.3 @@ -0,0 +1,27 @@
     1.4 +(*  Title: 	HOL/Hoare/Arith2.thy
     1.5 +    ID:         $Id$
     1.6 +    Author: 	Norbert Galm
     1.7 +    Copyright   1995 TUM
     1.8 +
     1.9 +More arithmetic.
    1.10 +*)
    1.11 +
    1.12 +Arith2 = Arith +
    1.13 +
    1.14 +consts
    1.15 +  divides :: "[nat, nat] => bool"			(infixl 70)
    1.16 +  cd	  :: "[nat, nat, nat] => bool"
    1.17 +  gcd	  :: "[nat, nat] => nat"
    1.18 +
    1.19 +  pow	  :: "[nat, nat] => nat"			(infixl 75)
    1.20 +  fac	  :: "nat => nat"
    1.21 +
    1.22 +defs
    1.23 +  divides_def	"x divides n == 0<n & 0<x & (n mod x) = 0"
    1.24 +  cd_def	"cd x m n  == x divides m & x divides n"
    1.25 +  gcd_def	"gcd m n     == @x.(cd x m n) & (!y.(cd y m n) --> y<=x)"
    1.26 +
    1.27 +  pow_def	"m pow n     == nat_rec n (Suc 0) (%u v.m*v)"
    1.28 +  fac_def	"fac m       == nat_rec m (Suc 0) (%u v.(Suc u)*v)"
    1.29 +
    1.30 +end