How to align the lines in a multiline equation while using the space optimally?

Question

I have a long equation with multiple equalities where I even have to split off the first equation.

• Using 'multline' breaks the alignment of the equations
• With 'align' or 'split' I have to pick an arbitrary point in the first line to align the others to. I also cannot align within \left(...\right).

Is there a way to do it automatically? I'm looking for something that looks like this picture in the end:

This is my code right now:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\newcommand{\pot}{\ensuremath{^{p/2}}}

\begin{equation}\begin{split}
    (t+\tau)\pot-C&\left(m\lor\sup_{s\leq\tau}|B_s+b|\right)^p\\
    &\leq t\pot+\tau\pot-C\sup_{s\leq\tau}|B_s+b|^p\\
    &\leq t\pot+\tau\pot-C\sup_{s\leq\tau}|B_s^p+b^p|\\
    &\leq t\pot+\tau\pot-C\sup_{s\leq\tau}\big||B_s|^p-|b|^p\big|\\
    &\leq t\pot+Cm^p+\tau\pot-CM_\tau^p\\
\end{split}\end{equation}
\end{document}

Answer 1

How about this, with multline and aligned:

\documentclass{article}
\usepackage{mathtools, nicefrac}
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.3pt}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\newcommand{\pot}{\ensuremath{^{p/2}}}

\begin{document}

\begin{multline}
    (t+\tau)\pot-C\Bigl(m\lor\sup_{s\leq\tau}\abs{B_s+b}\Bigr)^p\\
\begin{aligned}
    &\leq t\pot+\tau\pot-C\sup_{s\leq\tau}\abs{B_s+b}^p \leq t\pot+\tau\pot-C\sup_{s\leq\tau}\abs{B_s^p+b^p}\\
    &\leq t\pot+\tau\pot-C\sup_{s\leq\tau}\abs[\big]{\abs{B_s}^p-\abs{b}^p}\leq t\pot+Cm^p+\tau\pot-CM_\tau^p
\end{aligned}
\end{multline}

\end{document}

Answer 2

This is exactly what \MoveEqLeft from mathtools is for:

\documentclass{article}

\usepackage{mathtools}

\begin{document}

\newcommand{\pot}{\ensuremath{^{p/2}}}

\begin{equation}
  \begin{split}
    \MoveEqLeft
    (t+\tau)\pot-C\left(m\lor\sup_{s\leq\tau}|B_s+b|\right)^p\\
    &\leq t\pot+\tau\pot-C\sup_{s\leq\tau}|B_s+b|^p\\
    &\leq t\pot+\tau\pot-C\sup_{s\leq\tau}|B_s^p+b^p|\\
    &\leq t\pot+\tau\pot-C\sup_{s\leq\tau}\big||B_s|^p-|b|^p\big|\\
    &\leq t\po
t+Cm^p+\tau\pot-CM_\tau^p\\
  \end{split}
\end{equation}

\end{document}

By default \MoveEqLeft starts the first line 2em to the left of the alignment point of the other lines. If you write \MoveEqLeft[5] this will be changed to 5em, and so on.