1

As the the title suggests, I want to have something like Corollary 1.I (first corollary of the first chapter)

I want the chapter counter be in Arabic numbers, and the corollary counter be in Roman numbers.

Before, when I was using ntheorem, I used to use the command \theoremnumbering{Roman}.

I tried to read what thmtools documentation suggest, but I can't understand.

my corollary environment is simply defined as follows:

\declaretheorem[
    name=Corollary,
    numberwithin=chapter ]{cor}

If you can help me also with the equivalence of \theoremindent (it adds margin to the theorem environment). If there is not a simple equivalence, I will pose that as a separate question.

2

Once the Corollary environment cor is defined you can reset the number by redefining \thecor. In your case putting \show\thecor after the definition reveals

> \thecor=macro:
->\thechapter .\arabic {cor}.
l.9 \show\thecor

in the log file. So the format you wish for can be obtained by replacing \arabic by \Roman here as follows

 \renewcommand*{\thecor}{\thechapter.\Roman{cor}}

Sample output

\documentclass{book}

\usepackage{amsthm}
\usepackage{thmtools}

\declaretheorem[numberwithin=chapter]{theorem}

\declaretheorem[name=Corollary,numberwithin=chapter]{cor}
\renewcommand*{\thecor}{\thechapter.\Roman{cor}}

\declaretheorem[numberwithin=chapter]{lemma}

\begin{document}

\chapter{A chapter}

\begin{theorem}
  A theorem.
\end{theorem}

\begin{cor}
  A corollary.
\end{cor}

\begin{lemma}
  A lemma.
\end{lemma}

\begin{theorem}
  Another theorem.
\end{theorem}

\end{document}

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