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Idea:
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>;