Lemmas and sub sections

Question

I want to write a LaTeX code to show,

Lemma 1 : x+y=z
Lemma 1.1:  z-r+t=3
Lemma 1.2:   q=r

How do I do that?

Answer 1

Using amsthm package

Update: per Gonzalo Medina's suggestion, using the following definition which make the sublemma counter subsidiary to the lemma counter:

\newtheorem{lemma}{Lemma}
\newtheorem{sublemma}{Lemma}[lemma]

such that the following code:

\begin{lemma}
x+y=z
\end{lemma}
\begin{sublemma}
z-r+t=3
\end{sublemma}
\begin{sublemma}
q=r
\end{sublemma}

\begin{lemma}
x+y=z
\end{lemma}
\begin{sublemma}
z-r+t=3
\end{sublemma}
\begin{sublemma}
q=r
\end{sublemma}

will give you:

EDIT: If you want to number your theorem with correspondence to the section it belongs to, use these definition instead:

\newtheorem{lemma}{Lemma}
\newtheorem{sublemma}{Lemma}[section]

Then check out the example:

\section{Math}
\begin{document}
\begin{lemma}
x+y=z
\end{lemma}
\begin{sublemma}
z-r+t=3
\end{sublemma}
\begin{sublemma}
q=r
\end{sublemma}

\section{More Math}
\begin{lemma}
x+y=z
\end{lemma}
\begin{sublemma}
z-r+t=3
\end{sublemma}
\begin{sublemma}
q=r
\end{sublemma}

which gives you:

Answer 2

Once yoy have defined your structure for lemmas using, for example

\newtheorem{lemm}{Lemma}

you can define a new structure slemm and make the counter for this new structure subsidiary to the lemm counter using the second optional argument for \newtheorem:

\newtheorem{slemm}{Lemma}[lemm]

A complete example:

\documentclass{article}
\usepackage{amsthm}

\newtheorem{lemm}{Lemma}
\newtheorem{slemm}{Lemma}[lemm]

\begin{document}

\begin{lemm}
test
\end{lemm}
\begin{slemm}
test
\end{slemm}
\begin{slemm}
test
\end{slemm}
\begin{lemm}
test
\end{lemm}
\begin{slemm}
test
\end{slemm}
\begin{slemm}
test
\end{slemm}

\end{document}

For clarity sake, I would give another name to the subsidiary structure:

\documentclass{article}
\usepackage{amsthm}

\newtheorem{lemm}{Lemma}
\newtheorem{slemm}{Sublemma}[lemm]

\begin{document}

\begin{lemm}
test
\end{lemm}
\begin{slemm}
test
\end{slemm}
\begin{slemm}
test
\end{slemm}
\begin{lemm}
test
\end{lemm}
\begin{slemm}
test
\end{slemm}
\begin{slemm}
test
\end{slemm}

\end{document}

Answer 3

Is this what you are looking for?

\documentclass{article}
\usepackage{amsthm}
\theoremstyle{plain}
\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}[thm]{Lemma}
\begin{document}
\section{One}
\begin{lem}
  one
\end{lem}
\begin{lem}
  one.two
\end{lem}
\section{Two}
\begin{lem}
  two
\end{lem}
\end{document}