\documentclass{article}
\usepackage{amsmath}
\usepackage{amsthm}
\title{Exercise on equation and theorem-type environments }
\author{}
\date{}
\newtheorem{proposition}{Proposition}
\begin{document}
\maketitle
\begin{proposition}
Suppose that
$$
a=b.
$$
If in addition to (1) we have
$$
b=c,
$$
then $a=c$.
\end{proposition}
\begin{proof}
It follows from equations (1) and (2) that $a=c$.
\end{proof}
Proposition 1 is rather trivial.
\end{document}