theorem and subtheorem hierarchical numbering

Question

I want the numbering of claims, subclaims, subsubclaims, etc to be hierarchically numbered. Is there a way to do this without having to make those extra "subclaim" environments? For example:

\documentclass{article}
\usepackage{amsmath,amsthm,amssymb}
\newtheorem{thm}{Theorem}
\newtheorem{claim}{Claim}[thm]

\begin{document}
\begin{thm}
this has a long proof. i break it up into smaller claims.
\end{thm}

\begin{claim}
i prove a smaller piece of the theorem. 
this proof makes its own even smaller claims.
\end{claim}

\begin{claim}
i prove a claim made in the previous claim environment.
\end{claim}
\end{document}

This example produces the following numbering:

Theorem 1

Claim 1.1

Claim 1.2

Ideally, I would want the numbering to go like:

Theorem 1

Claim 1.1

Claim 1.1.1

since the last claim "belongs" to the claim before it.

Some of the solutions I've seen accomplish this by making an extra "subtheorems" wrapper environment. Is there a simpler way?

Answer 1

Maintaining a stack of such levels is not really easy. I tried to provide this down to six levels, which automatic backup etc. and up/down levelling if needed.

There's an issue with a reusage of the claim environment when \holdlevelfalse is used. I'll try to figure out this.

Use the command \claimhierarchies{claim}{6}{thm}, meaning six levels, the 'parent' level is thm. then.

\documentclass{article}
\usepackage{amsmath,amsthm,amssymb}


\usepackage{xparse}
\usepackage{xpatch}
\usepackage{chngcntr}%

\newtheorem{thm}{Theorem}

\newcounter{claimlevel}[thm]

\newtheorem{claim}{Claim}[thm]


\ExplSyntaxOn


\newcommand{\claimhierarchies}[3]{%
  \newcounter{#1i}
  \expandafter\renewcommand\csname the#1i\endcsname{\bfseries \csname the#3\endcsname.\arabic{#1i}}%
  \int_step_inline:nnnn {2}{1}{#2}{%
    \newcounter{#1\romannumeral##1}[#1\romannumeral\numexpr##1-1]
    \expandafter\renewcommand\csname the#1\romannumeral##1\endcsname{\csname the#1\romannumeral\numexpr ##1-1\endcsname.\arabic{#1\romannumeral\numexpr##1}}
  }
}

\seq_new:N \g_claimcounter_stack_seq


\newcommand{\pushcounter}[1]{%
  \seq_gpush:Nn \g_claimcounter_stack_seq {#1}
}  

\newcommand{\popcounter}[1]{%
  \seq_pop:NN \g_claimcounter_stack_seq \l_tmpa_tl
  \setcounter{#1}{\l_tmpa_tl}%
} 


\newcommand{\getcounter}[1]{%
  \seq_get:NN \g_claimcounter_stack_seq \l_tmpa_tl
  \setcounter{#1}{\l_tmpa_tl}%
} 

\ExplSyntaxOff




\makeatletter

\newif\ifholdlevel
\newif\iflevelup
\newif\ifverbose
\verbosetrue


\newcommand{\levelup}{%
  \ifnum\c@claimlevel > 1
  \addtocounter{claimlevel}{\m@ne}
  \ifverbose
  Level up to Level \Roman{claimlevel}
  \fi
  \leveluptrue
  \fi
}




\AtBeginEnvironment{claim}{%
  \iflevelup
  \csletcs{theclaim}{theclaim\romannumeral\numexpr\c@claimlevel}
  \csletcs{c@claim}{c@claim\romannumeral\c@claimlevel}
  \else
  \ifholdlevel
  \ifverbose
  Hold Level on Level \Roman{claimlevel}
  \fi
  \csletcs{theclaim}{theclaim\romannumeral\numexpr\c@claimlevel}
  \csletcs{c@claim}{c@claim\romannumeral\c@claimlevel}
  \else
  \addtocounter{claimlevel}{1}%
  \ifverbose
  Level down to Level \Roman{claimlevel}
  \fi
  \pushcounter{\number\value{claim}}%
  \csletcs{theclaim}{theclaim\romannumeral\numexpr\c@claimlevel} % 
  \csletcs{c@claim}{c@claim\romannumeral\c@claimlevel}
  \fi
  \fi
}

\makeatother


\claimhierarchies{claim}{6}{thm}


\begin{document}
\begin{thm}
this has a long proof. i break it up into smaller claims.
\end{thm}

\begin{claim}
i prove a smaller piece of the theorem. 
this proof makes its own even smaller claims.
\end{claim}

\begin{claim}
i prove a claim made in the previous claim environment.
\end{claim}


\begin{claim}
i prove a claim made in the previous claim environment.
\end{claim}


\begin{claim}
i prove a claim made in the previous claim environment.
\end{claim}


\holdleveltrue


\begin{claim}
i prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}
i prove a claim made in the previous claim environment.
\end{claim}


\levelup

\begin{claim}
i prove a claim made in the previous claim environment.
\end{claim}



\levelup

\begin{claim}
i prove a claim made in the previous claim environment.
\end{claim}

\holdleveltrue

\begin{claim}
i prove a claim made in the previous claim environment.
\end{claim}

\holdlevelfalse
\levelupfalse


\begin{claim}
i prove a claim made in the previous claim environment.
\end{claim}


\end{document}

Answer 2

The claim environment accepts an optional argument, default =, that's used to climb up or down a level. With + you go one level up, with - one level down; it's also possible to jump down two or three levels with -- and ---.

\documentclass{article}
\usepackage{amsthm,xparse,etoolbox}

\newtheorem{theorem}{Theorem}
\newtheorem{Claim}{Claim}[theorem]
\newtheorem{ClaimI}{Claim}[Claim]
\newtheorem{ClaimII}{Claim}[ClaimI]
\newtheorem{ClaimIII}{Claim}[ClaimII]
\newcounter{claimlevel}[theorem]

\ExplSyntaxOn
\NewDocumentEnvironment{claim}{O{=}}
 {
  \str_case:nn { #1 }
   {
    {=}  { }
    {+}  { \stepcounter{claimlevel} }
    {-}  { \addtocounter{claimlevel}{-1} }
    {--} { \addtocounter{claimlevel}{-2} }
    {---}{ \addtocounter{claimlevel}{-3} }
   }
  \begin{ Claim \int_to_Roman:n { \value{claimlevel} } }
 }
 {
  \end{ Claim \int_to_Roman:n { \value{claimlevel} } }
 }
\ExplSyntaxOff

\begin{document}

\begin{theorem}
This has a long proof. I break it up into smaller claims.
\end{theorem}

\begin{claim}
I prove a smaller piece of the theorem. 
This proof makes its own even smaller claims.
\end{claim}

\begin{claim}[+]
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}[+]
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}[-]
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}[-]
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}[+]
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}[-]
I prove a claim made in the previous claim environment.
\end{claim}


\begin{theorem}
This has a long proof. I break it up into smaller claims.
\end{theorem}

\begin{claim}
I prove a smaller piece of the theorem. 
This proof makes its own even smaller claims.
\end{claim}

\begin{claim}[+]
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}[+]
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}[--]
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}[+]
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}[+]
I prove a claim made in the previous claim environment.
\end{claim}

\begin{claim}[--]
I prove a claim made in the previous claim environment.
\end{claim}

\end{document}