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+\nopagenumbers
+\parindent=0pt
+\beginsection
+Product cancellation law
+
+For all $a,b,c\in Z$, if $a\ne 0$ and $a\cdot b=a\cdot c$, then $b=c$.
+
+\beginsection
+Trichotomy law
+
+For all $a\in Z$ exactly one of the following is true:
+$a\in N$, $a=0$ or $-a\in N$.
+
+\beginsection
+Well-ordering principle
+
+If $S$ is a nonempty subset of $N$, then there is an $a\in S$ such that
+$a\le b$ for every $b\in S$.
+
+\beginsection
+Division algorithm theorem
+
+If $a,b\in Z$ such that $a\ne 0$, then there is a unique $q$ and $r$
+such that $b=a\cdot q+r$ and $0\le r<|a|$.
+
+\beginsection
+Euclidean algorithm theorem
+
+Let $a,b\in Z$ such that $a\ne 0$ and $b\ne 0$.
+Then $gcd(a,b)$ exists and there are $x,y\in Z$ such that
+$gcd(a,b)=ax+by$.
+
+\end