Corollary 4

If $a$ and $b$ are integers such that $a \leqslant b$, then there exists a unique integer $c$ such that $b = a + c$.

The existence of $c$ follows from Proposition 13 of § 3, no. 6, and its uniqueness from Corollary 3 above.

¶ The integer $c$ such that $b = a + c$ (where $a \leqslant b$) is called the difference of the integers $b$ and $a$, and is written $b - a$. It is easily verified that if $a$, $b$, $a'$, $b'$ are integers such that $a \leqslant b$ and $a' \leqslant b'$, then