Problem with proof environment

I've written a proof in LaTeX, and I looked up how to use the proof environment. From what I read, it should start with "Proof:" and end with \qed, but the PDF shows no changes. It simply displays the text verbatim. What could be the cause of this? My code is as follows:

\documentclass[12pt]{report}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{graphicx}
\usepackage{float}
\usepackage{framed}
\usepackage[hang,flushmargin]{footmisc}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[theorem]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{definition}{Definition}[section]

\begin{document}
\begin{proof}
\noindent Assume that $R$ decides $HALT_{TM}$, and obtain a contradiction. Construct $S$ to decide $A_{TM}$, where $S$ operates as follows: \newline \newline
$S=$ On input $\langle M, w \rangle$, an encoding of a TM $M$ and a string $w$:
\begin{enumerate}
\item Run TM $r$ on input $\langle M, w \rangle$.
\item If $R$ rejects, reject
\item If $R$ accepts, accept
\item If $M$ has accepted, accept; if $M$ has rejected, reject."
\end{enumerate}

\noindent \newline If $R$ decides $HALT_{TM}$, then $S$ decides $A_{TM}$. Because $A_{TM}$ is undecidable, $HALT_{TM}$ must also be undecidable.
\end{proof}
\end{document}
• please fix your example to be a complete document that shows the problem. proof isn't defined by default but several packages define environments of this form so it is impossible to guess what definitions you are using. – David Carlisle Jul 5 '18 at 23:26
• Do you require a picture of the PDF? If so, how do I do that? – user83024 Jul 5 '18 at 23:30
• as posted the document produces the error ! LaTeX Error: Environment proof undefined. after an error you shouldn't really even look at the pdf, you need to fix the error first, – David Carlisle Jul 5 '18 at 23:33
• I'm not getting any errors. That's why I'm confused. – user83024 Jul 5 '18 at 23:34
• did you intend to load the amsthm package? – David Carlisle Jul 5 '18 at 23:34 The proof environment is not defined so you get the error

! LaTeX Error: Environment proof undefined.

a common way to define it is to load amsthm when you get a proof heading and qed box at the end.

\documentclass[12pt]{report}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{graphicx}
\usepackage{float}
\usepackage{framed}
\usepackage[hang,flushmargin]{footmisc}

\usepackage{amsthm}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[theorem]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{definition}{Definition}[section]

\begin{document}
\begin{proof}
Assume that $R$ decides $\mathrm{HALT}_{\mathrm{TM}}$, and obtain a contradiction. Construct $S$ to decide $A_{\mathrm{TM}}$, where $S$ operates as follows:

$S={}$ On input $\langle M, w \rangle$, an encoding of a TM $M$ and a string $w$:
\begin{enumerate}
\item Run TM $r$ on input $\langle M, w \rangle$.
\item If $R$ rejects, reject
\item If $R$ accepts, accept
\item If $M$ has accepted, accept; if $M$ has rejected, reject."
\end{enumerate}

If $R$ decides $\mathrm{HALT}_{\mathrm{TM}}$, then $S$ decides $A_{\mathrm{TM}}$. Because $A_{\mathrm{TM}}$ is undecidable, $\mathrm{HALT}_{\mathrm{TM}}$ must also be undecidable.
\end{proof}
\end{document}
• Thank you! I guess ShareLaTeX is missing some info. At least, from what I could see. – user83024 Jul 5 '18 at 23:52
• @user83024 i am sure that sharelatex is flagging errors if you look in the right place, also it can show you the log file which will also have the error message. I can't give details as I don't use it myself – David Carlisle Jul 5 '18 at 23:56