LaTeX Multiple alignment points in LaTeX

[Fredrik]

If I have two strings of equalities within the same align or alignat environment, and the first one is long enough to need two lines, I would want the result to look like

A+B+C=D=E
     =F=G=H
I=J

rather than

A+B+C=D=E
     =F=G=H
    I=J

Is there a way to do this? I suppose it can be done with an array, but I thought either align or alignat would be able to handle this. I get garbage results like these:

\begin{alignat}{3}
&F_k &=(f\chi_E)^{-1}(v_k)=\{x\in X|f(x)\chi_E(x)=v_k\}=\{x\in X|f(x)=v_k\}\cap E\\
&&=f^{-1}(v_k)\cap E=E_k\cap E\in\Sigma,\\
&\mu\big(F_k)=\mu(E_k\cap E)\leq\mu(E_k)<\infty.
\end{alignat}

\begin{alignat}{4}
&F_k && =(f\chi_E)^{-1}(v_k) =\{x\in X|f(x)\chi_E(x)=v_k\}=\{x\in X|f(x)=v_k\}\cap E\\
&&&=f^{-1}(v_k)\cap E=E_k\cap E\in\Sigma,\\
&\mu\big(F_k)=\mu(E_k\cap E)\leq\mu(E_k)<\infty.
\end{alignat}

 

[Wrichik Basu]

Have you tried using two separate \begin{align}...\end{align} environments? What you are trying to achieve, might not be possible within one environment.