Hendrik Vogt has provided a \longnot macro to alleviate the issues related to
Interaction of \boldmath and \not. This seems to work fine, but I run into a snag when I try to automatically use \longnot instead of the usual \not when I am in \bm mode.
This seemed like a very simple:
\let\not\longnot%
or
\def\not{\longnot}%
but these results in
TeX capacity exceeded, sorry [grouping levels=255]
The MWE as is yields:

When automated, the last \subseteq in red should be using the \longnot instead of \not.
Code:
\documentclass{article}
\usepackage[paperwidth=7cm]{geometry}
\usepackage{parskip}% Eliminate the need for \noindent
\usepackage{bm,xcolor}
% https://tex.stackexchange.com/questions/98433/interaction-of-boldmath-and-not
\newcommand*\longnot{%
\mathrel{%
\mkern-0.75mu
\raisebox{-0.8pt}{$\not$}%
\mkern1.5mu
\raisebox{0.8pt}{$\not$}%
\mkern-0.75mu
}
}
\newcommand{\ColorRed}[1]{%
%\let\not\longnot% Why can I NOT use one of these???
%\def\not{\longnot}%
\textcolor{red}{\bm{#1}}%
}%
\begin{document}
$\bm{A\not\subseteq B}$ versus $\bm{A\longnot\subseteq B}$
\par\smallskip
with color: \textcolor{red}{$\bm{R \longnot\subseteq T,\ x \longnot\le y$}}
Replace \verb|\not| with \verb|\longnot| when in \verb|\bm| mode:
$A \not\subseteq B$,
\ColorRed{$A \not\subseteq B$},
$A \not\subseteq B$.
\end{document}
\let\orignot\notand replace both\notby\orignotin the definition of\longnot, and after that all put\let\not\longnot? – yo' Feb 23 '13 at 01:15\begingroupand\endgroupin your\ColorRedso that the redefinition of\notbecomes local. – Hendrik Vogt Feb 23 '13 at 10:33