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forall x in Z, y in Z: x+y = y+x.Take arbitrary x0 in Z,y0 in Z. We have to show
x0+y0 = y0+x0.We know
x0+y0 = (definition of +) I(x0 +N y0, x1 +N y1) = (commutativity of +N) I(y0 +N x0, y1 +N x1) = (definition of +) y0+x0.