How To Reset Counter To Latest Theorem/Definition/Whatever?

Question

I like to give frequent examples and would like the numbering of these examples based on whatever definition/theorem/lemma/corollary/whatever was just shown. I would also like this numbering to be alphabetic if possible.

So for instance I would like the numbering on the examples below to be 1.1.1a, 1.1.1a, 1.1.2a, and 1.1.2b respectively.

Current Output:

Current TeX:

\documentclass[12pt, letterpaper]{article}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{chngcntr}
\renewcommand{\qedsymbol}{\rule{0.7em}{0.7em}}
\newcommand{\Mod}[1]{\ (\mathrm{mod}\ #1)}
\counterwithin{figure}{section}
\theoremstyle{definition}
\newtheorem{exmp}{Example}[subsection]
\newtheorem{theorem}{Theorem}[subsection]
\newtheorem{corollary}{Corollary}[theorem]
\newtheorem{definition}{Definition}[subsection]
\newtheorem{lemma}[section]{Lemma}
\numberwithin{equation}{section}

\begin{document}
\section{How To Add}
\subsection{A Detailed Look}

\begin{definition}
    \textbf{addition} is denoted with the + symbol
\end{definition}
\begin{exmp}
    1+0=1
\end{exmp}
\begin{theorem}
    \textbf{Trichotomy I:} The addition of two positives is positive.
\end{theorem}
\begin{exmp}
    Not sufficient since (-1)+2=1
\end{exmp}  
\begin{theorem}
    \textbf{Trichotomy II:} The addition of two negatives is negative.
\end{theorem}
\begin{exmp}
    (-1)+(-2)=-3
\end{exmp}
\begin{exmp}
    Not sufficient since (-2)+1=-1
\end{exmp}
\end{document}

Any ideas?

Answer 1

You can define an example counter "prefix", and this prefix is updated with the use of every environment that you may consider having examples following it.

\documentclass{article}

\usepackage{amsthm}
\usepackage{chngcntr}
\usepackage{etoolbox}

\theoremstyle{definition}
\newtheorem{theorem}{Theorem}[subsection]
\newtheorem{definition}{Definition}[subsection]
\newtheorem{exmp}{Example}

% Capture latest environment that could have an example following it
\AtEndEnvironment{theorem}{\global\let\exampleprefix\thetheorem}
\AtEndEnvironment{definition}{\global\let\exampleprefix\thedefinition}

% Adjust Example counter to be reset with every theorem, definition, ...
\counterwithin{exmp}{theorem}
\counterwithin{exmp}{definition}
% Update representation of Example counter
\newcommand{\exampleprefix}{}% Define Example counter prefix to be empty at first
\renewcommand{\theexmp}{\exampleprefix\alph{exmp}}% Prefix counter with whatever environment was used previously

\begin{document}

\section{How To Add}
\subsection{A Detailed Look}

\begin{definition}
\textbf{addition} is denoted with the + symbol
\end{definition}

\begin{exmp}
$1 + 0 = 1$
\end{exmp}

\begin{theorem}
\textbf{Trichotomy I:} The addition of two positives is positive.
\end{theorem}

\begin{exmp}
Not sufficient since $(-1) + 2 = 1$
\end{exmp}

\begin{theorem}
\textbf{Trichotomy II:} The addition of two negatives is negative.
\end{theorem}

\begin{exmp}
$(-1) + (-2) = -3$
\end{exmp}

\begin{exmp}
Not sufficient since $(-2) + 1 = -1$
\end{exmp}

\end{document}

Answer 2

Please, don't use independent numbering for theorems, definitions, lemmas and corollaries. Your reader won't be able to find them when you cross reference them by number.

And you'll have, in this case, two examples numbered 1.1.1a, making the numbering useless.

If you accept this advice, you just define exmp to have its counter tied to definition.

\documentclass{article}
\usepackage{amsthm}

\theoremstyle{definition}

\newtheorem{definition}{Definition}[subsection]
\newtheorem{theorem}[definition]{Theorem}
\newtheorem{corollary}[definition]{Corollary}
\newtheorem{lemma}[definition]{Lemma}
\newtheorem{exmp}{Example}
\counterwithin*{exmp}{definition}
\renewcommand{\theexmp}{\thedefinition\alph{exmp}}

\begin{document}

\section{How To Add}

\subsection{A Detailed Look}

\begin{definition}
    \textbf{addition} is denoted with the + symbol
\end{definition}
\begin{exmp}
    1+0=1
\end{exmp}
\begin{theorem}
    \textbf{Trichotomy I:} The addition of two positives is positive.
\end{theorem}
\begin{exmp}
    Not sufficient since (-1)+2=1
\end{exmp}  
\begin{theorem}
    \textbf{Trichotomy II:} The addition of two negatives is negative.
\end{theorem}
\begin{exmp}
    (-1)+(-2)=-3
\end{exmp}
\begin{exmp}
    Not sufficient since (-2)+1=-1
\end{exmp}

\subsection{A Check}

\begin{definition}
    \textbf{addition} is denoted with the + symbol
\end{definition}
\begin{exmp}
    1+0=1
\end{exmp}
\begin{theorem}
    \textbf{Trichotomy I:} The addition of two positives is positive.
\end{theorem}
\begin{exmp}
    Not sufficient since (-1)+2=1
\end{exmp}  
\begin{theorem}
    \textbf{Trichotomy II:} The addition of two negatives is negative.
\end{theorem}
\begin{exmp}
    (-1)+(-2)=-3
\end{exmp}
\begin{exmp}
    Not sufficient since (-2)+1=-1
\end{exmp}

\end{document}

Otherwise, with a slight modification of Werner's code:

\documentclass{article}
\usepackage{amsthm}

\theoremstyle{definition}

\newtheorem{definition}{Definition}[subsection]
\newtheorem{theorem}{Theorem}[subsection]
\newtheorem{corollary}{Corollary}[theorem]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{exmp}{Example}
\counterwithin*{exmp}{definition}
\counterwithin*{exmp}{theorem}
\counterwithin*{exmp}{lemma}
\counterwithin*{exmp}{corollary}
\renewcommand{\theexmp}{\thelaststatement\alph{exmp}}

\AtEndEnvironment{definition}{\xdef\thelaststatement{\thedefinition}}
\AtEndEnvironment{theorem}{\xdef\thelaststatement{\thetheorem}}
\AtEndEnvironment{corollary}{\xdef\thelaststatement{\thecorollary}}
\AtEndEnvironment{lemma}{\xdef\thelaststatement{\thelemma}}

\begin{document}

\section{How To Add}

\subsection{A Detailed Look}

\begin{definition}
    \textbf{addition} is denoted with the + symbol
\end{definition}
\begin{exmp}
    1+0=1
\end{exmp}
\begin{theorem}
    \textbf{Trichotomy I:} The addition of two positives is positive.
\end{theorem}
\begin{exmp}
    Not sufficient since (-1)+2=1
\end{exmp}  
\begin{theorem}
    \textbf{Trichotomy II:} The addition of two negatives is negative.
\end{theorem}
\begin{exmp}
    (-1)+(-2)=-3
\end{exmp}
\begin{exmp}
    Not sufficient since (-2)+1=-1
\end{exmp}

\subsection{A Check}

\begin{definition}
    \textbf{addition} is denoted with the + symbol
\end{definition}
\begin{exmp}
    1+0=1
\end{exmp}
\begin{theorem}
    \textbf{Trichotomy I:} The addition of two positives is positive.
\end{theorem}
\begin{exmp}
    Not sufficient since (-1)+2=1
\end{exmp}  
\begin{theorem}
    \textbf{Trichotomy II:} The addition of two negatives is negative.
\end{theorem}
\begin{exmp}
    (-1)+(-2)=-3
\end{exmp}
\begin{exmp}
    Not sufficient since (-2)+1=-1
\end{exmp}

\end{document}