# How to properly use the align environment within a theorem environment in Tex while handling whitespace issues?

I currently am trying to use the align environment to display equations within a lemma using a theorem environment. My code goes like:

\documentclass[10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{amsmath,amsfonts,fullpage,graphicx,setspace,tikz,amsthm,centernot,bbm,graphicx,caption,titling,relsize}

\newtheorem{lemma}{Lemma}

\begin{document}

\begin{lemma}[A Lemma Goes Here]
We claim the following in our lemma that the three mathematical forms are equal:
\begin{align*}
f(x) & = x^2 \\
&= x\cdot x \\
\end{align*}
Proof. \text{In Appendix}
\end{lemma}
\end{document}


The problem here is that too much white space exists between the proof/comment area in the bottom. I am unable to use \vspace or such to control this whitespace. Is there a better way of doing things here?

Don't use a "closing \\" at the end of an align environment. Also, use the proof environment supplied by amsthm:

\documentclass{article}

\usepackage{amsmath,amsthm}

\newtheorem{lemma}{Lemma}

\begin{document}

\begin{lemma}[A Lemma Goes Here]
We claim the following in our lemma that the three mathematical forms are equal:
\begin{align*}
f(x) &= x^2 \\
&= x \cdot x
\end{align*}
\end{lemma}

\begin{proof}
In Appendix.
\end{proof}

\end{document}