Style inheritance in thmtools

[noib3]

Relevant tex.stackexchange post: https://tex.stackexchange.com/q/565165/172923.

[muzimuzhi]

Yes I've noticed the question on TeX-SX days before. Not sure if I can add this utility soon.

[noib3]

@muzimuzhi I think I had linked the wrong post. I've updated it now.

[mbertucci47]

A very simple attempt with almost no testing:

\documentclass{article}
\usepackage{amsthm,thmtools,xcolor}

\makeatletter

\define@key{thmstyle}{style}{%
  \thmt@inheritstyle{#1}%
}

\def\thmt@inheritstyle#1{
  \ifcsname thmt@style@#1@setdefaultkeys\endcsname%
  \csname thmt@style@#1@setdefaultkeys\endcsname%
  \else
  \PackageError{thmtools}{No style `#1' defined}{}%
  \fi
}

\renewcommand\declaretheoremstyle[2][]{%
  \def\thmt@style{#2}%
  \@xa\def\csname thmt@style \thmt@style @defaultkeys\endcsname{}%
  \thmt@declaretheoremstyle@setup
  \kvsetkeys{thmstyle}{#1}%
  \thmt@declaretheoremstyle{#2}%
  \@xa\def\csname thmt@style@\thmt@style @setdefaultkeys\endcsname{% ADDED
    \kvsetkeys{thmstyle}{#1}% ADDED
  }% ADDED
}

\def\thmt@style@plain@setdefaultkeys{}

\def\thmt@style@definition@setdefaultkeys{%
  \kvsetkeys{thmstyle}{%
    bodyfont=\normalfont
  }%
}

\def\thmt@style@remark@setdefaultkeys{%
  \kvsetkeys{thmstyle}{%
    spaceabove=0.5\topsep,
    spacebelow=0.5\topsep,
    headfont=\itshape,
    bodyfont=\normalfont
  }%
}

\makeatother

\declaretheoremstyle[
	headfont=\bfseries\color{blue},
	bodyfont=\itshape\color{red},
	headformat = \NUMBER\ \NOTE\ \NAME
	]{thmsty}
\declaretheoremstyle[
	style=thmsty,
	notebraces={[}{]},
	bodyfont=\upshape\color{purple}
	]{lemsty}

\declaretheorem[style=thmsty]{theorem}
\declaretheorem[style=lemsty]{lemma}

\begin{document}

\begin{theorem}[heading]
Text
\end{theorem}

\begin{lemma}[heading]
Text
\end{lemma}

\end{document}

Might be better to give it a name like inherit-style.