Negative of Integer

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Theorem

Let $x \in \Z$ be an integer.

Let $x = \eqclass {a, b} {}$ be defined from the formal definition of integers, where $\eqclass {a, b} {}$ is an equivalence class of ordered pairs of natural numbers.

Then:

$-x = \eqclass {b, a} {}$


Proof

Follows from Inverse for Integer Addition.