Align formulas independently nested

Question

I have the formula

which I create with the code

\begin{align}
\WKernSub[\x]{sub} &\defas \bigsumshort \sum_{j=1\ |\ j\in\J}^{\card\Ob} \mhsp \frac{\massSub[j]{subA}}{\sqrt{ (2\m\pi\m\gwp)^{\nbFeat} }} \m \exp{ \frac{    \left(\x-\ob[j]\right)^\trnsp \m \left(\x-\ob[j]\right)   }{-2 \m \gwp} }  \mhspE,
\end{align}
\begin{align}
\J = \big\{\mhsp l \mhsp\big|\mhsp      &(  \ob\in\Obrd \AND l=i  ) \\
                                    \OR &(  \ob\in\Obru \AND \ob[l]\in\Obvd \AND \ob[l]\primderL\ob[i]  ) \mhsp\big\}  \mhspE,  \nn
\end{align}
\begin{align}
\WFctSub[\x]{sub} &\defas \bigsumshort \sum_{j=1\ |\ \ob[j]\in\Obr}^{\card\Ob} \WKernSub[\x]{sub} \label{eq:WKernSub}
\end{align}

What I would like is, to have the formulas aligned such, that the = and := are aligned. I do not want to have the alignment of the second formula touched. I did checkout Alignment across nested aligned environments, but I was not able to transfer this to my problem and Multiple aligning symbols. I don't want to "open" a new column for alignments.

How can I achieve this?

A minimal working example would be (other symbols):

\documentclass[twocolumn]{article}
\usepackage{amsmath}

\begin{document}

\begin{align}
W_{sub,i} &= asdf
\end{align}

\begin{align}
J = \big\{ l \quad\big|\quad    &(  o \in O ) \nonumber\\
                    \vee\quad   &(  o \in O \wedge o \in O  ) \big\}  , \nonumber
\end{align}

\begin{align}
W_{sub} &= some long formula without any meaning
\end{align}

\end{document}

resulting in

Answer 1

I's use a nested aligned (It is best never to have one math display following another, TeX doesn't really try to space that correctly)

\documentclass[twocolumn]{article}
\usepackage{amsmath}

\begin{document}

\begin{align}
W_{\mathrm{sub},i} &= asdf\\
&\begin{aligned}
J = \big\{ l \quad\big|\quad    &(  o \in O ) \nonumber\\
                    \vee\quad   &(  o \in O \wedge o \in O  ) \big\}  , \nonumber
\end{aligned}\\
W_{\mathrm{sub}} &= some long formula without any meaning
\end{align}

\end{document}

Answer 2

this is a kludge. it would have been much easier had you provided the definitions of the macros you used. the definitions and other coding here is just an approximation.

like david's answer, this nests an aligned block within the main alignment. the definition of the := is jiggered a bit to improve its alignment relative to that of the simple = signs.

\documentclass[leqno]{article}
\usepackage{mathtools}
\usepackage{bm}

\newcommand{\card}{\#}
\newcommand{\defas}{\;\mathrel{\!\!{:}{=}\,}}
\newcommand{\bigsumshort}{}
\newcommand{\gwp}{\omega}
\newcommand{\J}{\mathcal{J}}
\newcommand{\Ob}{\mathcal{O}}
\newcommand{\Obr}{\mathcal{O}_{\mathrm{r}}}
\newcommand{\Obrd}{\mathcal{O}_{\mathrm{rd}}}
\newcommand{\Obru}{\mathcal{O}_{\mathrm{ru}}}
\newcommand{\ob}{\bm{o}_{i}}
\newcommand{\m}{\cdot}
\newcommand{\mhsp}{}
\newcommand{\mhspE}{\;}
\newcommand{\massSub}[1]{m_{\mathrm{subA,v,#1}}}
\newcommand{\nbFeat}{F}
\newcommand{\trnsp}{\top}
\newcommand{\x}{\bm{x}}

\begin{document}

\begin{align}
\mathbf{W}_{\mathrm{sub}j} (\bm{x})
 &\defas \bigsumshort \sum_{j=1\ |\ j\in\J}^{\card\Ob} \mhsp
  \frac{\massSub{j}}{\sqrt{ (2\m\pi\m\gwp)^{\nbFeat} }} \m
  \exp \left( \frac{    \left(\x-\ob[j]\right)^\trnsp \m \left(\x-\ob[j]\right)   }{-2 \m \gwp} \right) \mhspE,\\
%
J &= \bigl\{ l \; \bigl| \;
           \begin{aligned}[t]
                  &( \ob \in \Obrd \wedge l = i ) \\
               \mathllap{\vee\,}   &( \ob \in \Obru \wedge \ob \in \Obrd
               \wedge \ob \leftarrow \ob  ) \bigr| \bigr\}  ,
           \end{aligned} \nonumber\\
%\J &= \big\{\mhsp l \mhsp\big|\mhsp      &(  \ob\in\Obrd \AND l=i  ) \\
%%                                    \OR &(  \ob\in\Obru \AND \ob[l]\in\Obvd \AND \ob[l]\primderL\ob[i]  ) \mhsp\big\}  \mhspE,  \nn\\
%
\mathbf{WF}_{\mathrm{sub}}(\x) &\defas \bigsumshort \sum_{j=1\ |\ \ob[j]\in\Obr}^{\card\Ob} \mathbf{W}_{\mathrm{sub}j}(\x) \label{eq:WKernSub}\\
%
W_{sub,i} &= asdf\\
%
W_{sub} &= some long formula without any meaning
\end{align}

\end{document}