\align环境中\text靠右排版

看看下面的代码：

\documentclass{article}
\usepackage{mathtools}
\usepackage{eqparbox}
\usepackage[showframe]{geometry}

\begin{document}

  \begin{flalign}
  & & a &= bbbbbb &\nonumber \\
 & & cccc & = dd & \text{(using Eq. 1)} & \nonumber \\
 & & e &= f & \text{(using Thm. 2)}
  \end{flalign}

  \begin{flalign}
  & & a &= bbbbbb \nonumber \\
 & & cccc & = dd & \eqparbox{C}{(using Eq. 1)} & \nonumber \\
 & & e &= f & \eqparbox{C}{(using Thm. 2)}
 \end{flalign}

\end{document} 

除去by lemma后，如果只有两列对齐的情况下，在\text{(by Lemma)}前简单地添加&&即可。

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{align*}
    c^2 &= a^2 + b^2 \\
        &= a^2 + b^2 \\
        &&\text{(by Lemma)}\\
        &= a^2 + b^2 \\
\end{align*}

\end{document}

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{subequations}
\begin{align*}
\| S+T \|^{2}_{A} & = \omega ^{2}_{A}(S+T)                                                   \\
                  & \leq \sup_{\substack{\|x\|_{A}=1}}(|\langle (S+iT)x,x \rangle _{A} |^{2} \\
\shortintertext{\hfill(by Lemma)}
                  & \leq \sup_{\substack{\|x\|_{A}=1}}(|\langle (S+iT)x,x \rangle _{A} |^{2} \\
\end{align*}
\end{subequations}
\end{document}

\documentclass{article}
\usepackage{calc}
\usepackage{amsmath}
\begin{document}

\begin{align*}
  M ={}    & a_1 + a_2 + a_3 + a_4 + a_5 + a_6 \\
           & \makebox[\widthof{$a_1 + a_2 + a_3 + a_4 + a_5 + a_6$}][r]{(by lemma)} \\
    \leq{} & b_1 + b_2 + b_3 + b_4 + b_5
\end{align*}

\end{document}

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{alignat*}{3}
&& \| S+T \|^{2}_{A}& = \omega ^{2}_{A}(S+T)                                        && \\
&&                  & \leq \sup_{\|x\|_{A}=1}(|\langle (S+iT)x,x \rangle _{A} |^{2} && \\
&&                  &                                     & \text{\llap{(by Lemma)}} & \\
&&                  & \leq \sup_{\|x\|_{A}=1}(|\langle (S+iT)x,x \rangle _{A} |^{2} && \\
\end{alignat*}

\end{document}