Alignment problem using align environement and \phantom

Question

The following code

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

\begin{document}
\begin{align*}
  A &\leq B \cdot C \cdot \int D
  \\&
    \phantom{{} \leq B \cdot {}}
    C \cdot \int D
  \\&
    \phantom{{} \leq B \cdot C {}}
    \cdot \int D
  \\&
    \phantom{{} \leq B \cdot C \cdot \int {}}
    D
\end{align*}

\begin{align*}
  A &\leq \fbox{aaaaaaaaaaaaaaaaaaaaaaaaa}
  \\&
    \phantom{{} \leq {}}
    \cdot \int \fbox{bbbbbbbbbbbbbbbb}
  \\&
    \phantom{{} \leq \cdot \int {}}
    \fbox{ccccccccccccccccccc}
\end{align*}
\end{document}

gives

In the first case the alignments work exactly as I would expect. But why in the second case the boxes of b's and c's are not aligned?

Answer 1

In the second align you're forgetting the empty atom after \leq:

\begin{align*}
  A &\leq \fbox{aaaaaaaaaaaaaaaaaaaaaaaaa}
  \\&
    \phantom{{} \leq {}}
    \cdot \int \fbox{bbbbbbbbbbbbbbbb}
  \\&
    \phantom{{} \leq {}\cdot \int {}}
    \fbox{ccccccccccccccccccc}
\end{align*}

When you have Rel Bin Op, the Bin atom is changed into Ord (think to $a \leq -\log b$), so the spacing changes.

Answer 2

Why don't you align it directly to the point where you want it, and then adjust the first row accordingly?

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

\begin{document}
\begin{align*}
  A \leq B \cdot C \cdot \int &D
  \\
  C \cdot \int &D
  \\
  \cdot \int &D
  \\
  &D
\end{align*}

\begin{align*}
   A \leq \hspace{2.2em} &\hspace{-2em}\fbox{aaaaaaaaaaaaaaaaaaaaaaaaa}
  \\
    \cdot \int &\fbox{bbbbbbbbbbbbbbbb}
  \\
    &\fbox{ccccccccccccccccccc}
\end{align*}
\end{document}

Please not that I added 2.2em before the &, instead of 2em, because it gives a space between the \leq and the box, and it looks a bit better, at least to me.