\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}