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Definition

Idea:

• Representation: let <a, b> denote the difference between a and b.
• Normalize: <a, 0_N> for non-negative ints, <0_N, a> for negative ones.

Z:= Z >= 0 union Z< 0;

Z >= 0 := {<x, 0N>: x in N};

Z< 0 := {<0N, x>: x in N\{0N}};

Constructor function:

I: N x N -> Z

I(x, y) := if x >= N y then <x-Ny, 0N> else <0N, y-Nx>;