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Integer Arithmetic

0 := [<0N, 0N>]; 1 := [<1N, 0N>]; 2 := [<2N, 0N>]

x := such a in N x N: x = [a]

x + y	:=	[<x0+Ny0,x1+Ny1>]
- x	:=	[<x1,x0>]
x - y	:=	[<x0+Ny1,y0+Nx1>]
x * y	:=	[<(x0*Ny0)+N(x1*Ny1), (x0*Ny1)+N(x1*Ny0)>]
x <= y	: <=>	x0+y1 <= N y0+x1

Since ~ _Z is a congruence relation, functions are uniquely defined.