undesired extra space above `\proof`

Question

In Theorems 1 and 2, there is extra space between the equation and the proof. In Theorem 3, there isn't. What is causing this in the case of Theorem 2 and how can I get the \proof command not to insert the extra space (without resorting to negative vspace)? I wish to learn about the mechanics (I'm not looking for a package that colors my equations: I'm aware of those).

\documentclass{article}

\usepackage{amsthm,xcolor}
\newtheorem{theorem}{Theorem}


\begin{document}



\begin{theorem}
    blabla
    {\color{red}
    \begin{equation} 
    x
    \end{equation}}%
    \proof
    hi  
\end{theorem}

\begin{theorem}
    blabla
    \begin{equation} \color{red}
    x
    \end{equation}
    \proof
    hi  
\end{theorem}


\begin{theorem}
    blabla
        \begin{equation} {\color{red}
        x}
        \end{equation}%
    \proof
    hi  
\end{theorem}
\end{document}

Answer 1

The package amsthm provides a proof environment. For implementation reasons, the command \proof exists, but should not be used in a document, because it opens an internal trivlist environment which is not properly closed.

Besides, the proof doesn't belong to the statement, so the environment should go outside theorem.

In order to color (part of) an equation, use \textcolor{<color>}{<math>}.

So the correct way to input the thing is

\documentclass{article}

\usepackage{amsthm,xcolor}

\newtheorem{theorem}{Theorem}

\begin{document}

\begin{theorem}
blabla
\begin{equation}
\textcolor{red}{x}
\end{equation}
\end{theorem}

\begin{proof}
hi
\end{proof}

\end{document}

which has no strange spacing, as you can clearly see.

If you don't want the “tombstone” (aka “end-of-proof symbol”), just add

\renewcommand{\qedsymbol}{}

before \begin{document}.

This said, you're free to shoot on your own foot, but using unsupported commands or syntax is, well, unsupported.