Referring to theorems

Question

I have the following: I have a lemma whose "number" as of yet is not certain (right now it's Lemma 0.1), and then a theorem in which I wish to refer to this lemma X, "let such and such be as in Lemma X". I could write "...as in Lemma 0.1" and change it once I'm done with the thesis, but is there a way to refer to lemma 0.1 so that if (when) it becomes, say, lemma 5.2, so that when this changes, my reference in the theorem also changes?

Wonderful wording, hope you get the point :P

Answer 1

For fuller details, take a look in some form of LaTeX documentation, for example Section 2.8 of the Not so short guide to LaTeX2e.

Here's an example of use:

In Lemma~\ref{lem:amazingLemma} we will prove something amazing.

\begin{lemma}
\label{lem:amazingLemma}
This is amazing.
\end{lemma}

\begin{theorem}
Under the conditions of Lemma~\ref{lem:amazingLemma} then things are amazing.
\end{theorem}

Important points:

1. You can refer to a label before or after it is defined, but it may take two compilations for LaTeX to get all the numbers straight.
2. The \label command has to go inside the environment, otherwise it will pick up something else (probably the last section declaration).
3. There are a variety of packages that enhance the cross-referencing system, for example making it so that your reference remembers whether it was a Lemma or a Proposition. If you look at the links under the "Related" column on the right-hand side of this page you'll get a feeling for what is possible with cross-referencing.
4. Just about anything with a counter can be labelled in this way.

Answer 2

Here's a working example:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage{graphicx}
\usepackage{amsmath} 

\newtheorem{lemma}{Lemma}
\newtheorem{theorem}{Theorem}

\begin{document}

\begin{lemma}
    \label{LeftCosetsDisjoint}
    Let $H$ be a subgroup of a group $G$, and let $x$ and $y$ be
    elements of $G$.  Suppose that $xH \cap yH$ is non-empty.
    Then $xH = yH$.
\end{lemma}

\begin{theorem}
    \label{MyTheorem}
    Let such and such be as in Lemma \ref{LeftCosetsDisjoint}
\end{theorem}

\end{document}

Answer 3

You have to label the destination to which you want to point with (in the corresponding line/block)

\label{name}

and then refer to it with

\ref{name}

It is usually a good idea to add some sort of specifier to the name (as Andrew Stacey did in his comment) - some examples are here in the introduction: http://en.wikibooks.org/wiki/LaTeX/Labels_and_Cross-referencing

I use different macros for every type (e.g. \imgref{...} and \eqref{...}) - makes stuff simpler in the long term (as bracket-type/color/... can be changed easily from one location.

Example:

\documentclass{article}
\usepackage{amssymb}
\newcommand{\eqRef}[1]{(\ref{eq:#1})}
\begin{document}
\begin{equation}
1 + 1 = 2\label{eq:calc}
\end{equation}
Some serious calculation was done in \eqRef{calc}
\end{document}