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\documentclass{math215}

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\usepackage{times,txfonts}

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\doclabel{Math 215: Homework 13a}
\docauthor{Your name here}
\docdate{April 24, 2013}

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\input{math215extras.tex}

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\begin{document}

\begin{proposition}{9.18}  For all $m,n\in\Ints$, 
\[
e(m\cdot n) = e(m)\cdot e(n).
\]
\end{proposition}
\begin{proof}
Your proof goes here.  Attempt maximal laziness.
\end{proof}

\begin{lemma}{11.A} Suppose $a,b\in\Ints$ and $b\neq 0$. Let $g=\gcd(a,b)$,
so $g\in\Nats$, $g\mid a$ and $g\mid b$.  Then
\[
\gcd\left(\frac{a}{g},\frac{b}{g}\right)=1.
\]
\end{lemma}
\begin{proof}
Recall that if $c\mid d$, and $c\neq 0$, then $\frac{c}{d}$ is
the unique integer $j$ such that $c=jd$.

Feel free to use Proposition 6.30!
\end{proof}

\begin{proposition}{8.50} If the sets $A$ and $B$ are bounded
  above and non-empty, and if $A\subseteq B$, then $\sup A\le \sup B$.
\end{proposition}
\begin{proof} Your proof goes here.
\end{proof}

\end{document}