Proof Environment – How to Create a ‘Proof of Theorem x.xx’ Header

Question

In many papers in mathematics, the author states a theorem in somewhere and adds some explanations and perhaps some lemmas and later starts the proof with a phrase like "Proof of Theorem x.xx" (x's stand for some numbers). The only format I am aware for starting and ending a proof is as follows:

\begin{proof}

\end{proof}

This format is good when I start the proof immediately after stating theorems (propositions etc). So my question is:

How can I start the proof later with a phrase like "Proof of Theorem x.xx"?

P.S. I am not sure about the tags I have used. Please, modify them if you know better tags.

Answer 1

Assuming you're using a package such as amsthm, you could proceed as follows: Assign a \label to the theorem, and then cross-reference it via a \ref statement at the start of the associated proof environment.

\documentclass{article}
\usepackage{amsthm}
\usepackage{lipsum} % for filler text
\newtheorem{theorem}{Theorem}
\begin{document}

\begin{theorem}[Pythagoras] \label{thm:neat}
$a^2+b^2=c^2$.
\end{theorem}

\lipsum[2]

\begin{proof}[Proof of Theorem \ref{thm:neat}]
(state your proof here)
\end{proof}

\end{document}

---

Addendum: For comparison, here's the output of the same MWE (minus the filler text) if you were to use the ntheorem package. (Observe that ntheorem doesn't automatically place a QED symbol at the end of a proof environment.)

\documentclass{article}
\usepackage{ntheorem}
\newtheorem{theorem}{Theorem}
\theoremstyle{empty}
\newtheorem{refproof}{Proof}
\begin{document}
\begin{theorem}[Pythagoras] \label{thm:neat}
$a^2+b^2=c^2$.
\end{theorem}

\begin{refproof}[Proof of Theorem \ref{thm:neat}]
(state your proof here)
\end{refproof}
\end{document}