Proper etiquette for using a lemma in a series of equations?

Suppose we have something like:

$$\begin{split} a &< b \\ ab &< bc \\ abc &> bcd \\ abcd &> bcde \end{split}$$


And to get the third line, abc &> bcd, a lemma previously stated in the document is being used. What is the proper way to denote this justification in here? Is there a way to insert/append a note at the end of the third line that says (Lemma 9) or something similar (if the lemma being used is numbered 9 earlier in the document)?

• There are many ways of doing this. How do you want it to look? Should the "label" be on the left, or right? Should be spaced just so away from the equation, or flush with the margin? Do you want the other equations in this set numbered as well? Also, you can't use the construction you have in your code snippet to present a multi-line equation... you're probably referring to something like align from amsmath. – Werner Mar 8 '15 at 1:48
• @Werner Is there a conventional way to do this with AMS math papers? – mr eyeglasses Mar 8 '15 at 1:49
• I would merely use \quad \text{(Lemma~\ref{<lemma>})}. – Werner Mar 8 '15 at 2:14

This is one way

\documentclass{article}
\usepackage{amsmath,amsthm}
\newtheorem{lemma}{Lemma}
\begin{document}
\begin{lemma}\label{lem:mylemma}
Some lemma
\end{lemma}
Some text here
$$\begin{split} a &< b \\ ab &< bc \\ abc &> bcd \qquad\qquad \rlap{\text{from Lemma~\ref{lem:mylemma}}} \\ abcd &> bcde \end{split}$$
\end{document}


• I would not recommend this in writing. Better to insert it via \intertext. – daleif Mar 8 '15 at 14:06

Here are 4 possibilities, with the alignat or flalign environment, and the \llap command:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[showframe]{geometry}

\usepackage{mathtools}

\begin{document}

Text text text text text text text text text text text text text text text text text text text text text text text text text.
\begin{alignat}{2}
a &< b \\
ab & < bc & & \text{by transitivity} \\
abc & > bcd & \hskip4em & \text{according to lemma 2} \\
abcd &> bcde
\end{alignat}
\begin{alignat}{2}
a &< b \\
ab & < bc & & \llap{by transitivity} \\
abc & > bcd & \hskip12em & \llap{according to lemma 2} \\
abcd &> bcde
\end{alignat}

\begin{flalign}
& & a &< b \\
& & ab &< bc & & \text{by transitivity}\\
& & abc &> bcd & & \text{according to lemma 2}\\
& & abcd &> bcde
\end{flalign}

\begin{flalign}
& & a &< b \\
& & ab &< bc & & \llap{by transitivity } \\
& & abc &> bcd & &\llap{according to lemma 2 }\\
& & abcd &> bcde
\end{flalign}

\end{document}


• Please don't recommend arguing or typesetting like this. It ends up looking horrible. – daleif Mar 8 '15 at 14:06
• @daleif: I agree the set of all $4$ possibilities is horrible, but each of them individually is conceivable — as often it depends on the context. I just wanted to give a sample of what can be done. – Bernard Mar 8 '15 at 14:19