How to number Corollaries by Lemmas

Question

I am looking to number my corollaries similarly to how Serre does it. His corollary numbers mirror the Lemma or Proposition which they follow. For example:

Section 1
Proposition 1
Corollary 1
Lemma 1.1
Corollary 1.1

Section 2
Lemma 2.1
Proposition 2
Lemma 2.2
Corollary 2.2A
Corollary 2.2B

How to do something similar in LaTeX? I am thinking something along the lines of:

\begin{lem}\label{l1}
...
\end{lem}
\begin{cor}\label{c1}\tag{\ref{l1}}
...
\end{cor}

However, this gives me a syntax error. [see full code below]

I also tried using reptheorem for this; however, it does not seem to be quite suited to this task; and I am not good enough at LaTeX coding to modify it to make it work here.

\documentclass[11pt]{amsart}
\usepackage{amsmath}
\newtheorem{lem}{Lemma}
\newtheorem{Lem}[lem]{Lemma}%*
\numberwithin{lem}{section}
\newtheorem{prop}{Proposition}
\newtheorem{Prop}[prop]{Proposition}
\newtheorem{Cor}{Corollary}%}[lem]{
\newtheorem{cor}[Cor]{Corollary}%*
\begin{document}
\section{asdf}
\begin{lem}\label{l1}
\end{lem}
\begin{prop}\label{p1}
\end{prop}
\begin{cor}\label{c1}\tag{\ref{l1}}
\end{cor}
\section{fdsa}
\begin{lem}\label{l2}
\end{lem}
\begin{prop}\label{p2}
\end{prop}
\begin{lem}\label{l2}
\end{lem}
\begin{cor}\label{c2}\tag{\ref{l2}A}
%\tag{asdf}
\end{cor}
\begin{cor}\label{c3}\tag{\ref{l2}B}
%\tag{asdf}
\end{cor}
\end{document}

Answer 1

Got it! With a modification to reptheorem.

\documentclass[11pt]{amsart}
\usepackage{amsmath}

\makeatletter
\newtheorem*{rep@theorem}{\rep@title}
\newcommand{\newreptheorem}[2]{%
\newenvironment{rep#1}[2][]{%
 \def\rep@title{#2 \ref{##2}##1}%
 \begin{rep@theorem}}%
 {\end{rep@theorem}}}
\makeatother

\newtheorem{lem}{Lemma}
\newreptheorem{lem}{Corollary}
\newtheorem{Lem}[lem]{Lemma}%*
\numberwithin{lem}{section}
\newtheorem{prop}{Proposition}
\newreptheorem{prop}{Corollary}
\newtheorem{Prop}[prop]{Proposition}
\newtheorem{Cor}{Corollary}%}[lem]{
\newtheorem{cor}[Cor]{Corollary}%*
\begin{document}
\section{asdf}
\begin{lem}\label{l1}
\end{lem}
\begin{prop}\label{p1}
\end{prop}
\begin{repprop}{p1}
\end{repprop}
\section{fdsa}
\begin{lem}\label{l2}
\end{lem}
\begin{prop}\label{p2}
\end{prop}
\begin{lem}\label{l2}
\end{lem}
\begin{replem}[A]{l2}
\end{replem}
\begin{replem}[B]{l2}
\end{replem}
\end{document}

Answer 2

Here's an implementation, which might be improved for cross-references.

\documentclass{amsart}

\newtheorem{propT}{Proposition}
\newtheorem{lemmaT}{Lemma}[section]
\newtheorem*{genericT}{\genericTname}

\newenvironment{prop}{\propT}{\endpropT\xdef\laststatement{\thepropT}}
\newenvironment{lem}{\lemmaT}{\endlemmaT\xdef\laststatement{\thelemmaT}}

\newenvironment{corollary}[1][]
 {\def\genericTname{Corollary \laststatement#1}\genericT}
 {\endgenericT}

\begin{document}

\section{asdf}
\begin{prop}
\end{prop}
\begin{corollary}
\end{corollary}
\begin{lem}
\end{lem}
\begin{corollary}
\end{corollary}

\section{fdsa}
\begin{lem}
\end{lem}
\begin{prop}
\end{prop}
\begin{lem}
\end{lem}
\begin{corollary}[A]
\end{corollary}
\begin{corollary}[B]
\end{corollary}
\end{document}

Personal comment. With due respect to one of the greatest mathematicians of the 20th century, this numbering scheme is silly. Especially devised for making it difficult to find a statement from a reference in the text: for instance, where the h*** will Proposition 24 be? Now add theorems: can you tell whether Proposition 18 is before or after Theorem 3? No, of course: you have no clue even about what section they are in. However, I've seen worse systems.

Addition

If you want to refer to corollaries with \label, I think this can work. Change the definition of corollary into

\makeatletter
\newenvironment{corollary}[1][]
 {%
  \def\genericTname{Corollary \laststatement#1}%
  \edef\@currentlabel{\laststatement#1}%
  \genericT
 }
 {\endgenericT}
\makeatletter

Now

\begin{corollary}[B]\label{whatever}

should make it possible to use \ref{whatever} and get “2.2B” (assuming the numbering of the example above).