Integland practice, cnt. 2

Negative operation Neg(x)

Let’s define unary operation  Neg : Z → Z  as follows:

x ∈ Z   Neg(x) := 0 – x

Thus

Neg(0)  =  0

THEOREM 2   ∀x y ∈ Z   Neg(x-y) = y-x

PROOF

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END of PROOF

As a corollary we get:
THEOREM 3   ∀x ∈ Z   Neg(Neg(x)) = x

PROOF

Neg(Neg(x))  =  Neg(0-x)  =  x-0  =  x

END of PROOF

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