I get "already defined" error when using `amsthm` package with `import`

Question

I use import command to modulize my chapters.
I also use amsthm package to define my own theorem environment.
When I try to compile the main (root) file, I get the following errors:
Command thm already defined. ...bered,vlined]{algorithm2e}newtheorem {thm}
Command lem already defined. ...em {thm}{Theorem}[section]newtheorem {lem}
Command cor already defined. ...orem {lem}{Lemma}[section]newtheorem {cor}
Command dfn already defined. ...theoremstyle {definition}newtheorem {dfn}
Command rem already defined. ...ion}theoremstyle {remark}newtheorem {rem}

I have to redefine them for every subfile because I want to compile and view the output for them independently.
My source files are as follows:
Root:
%%temp.tex
documentclass[12pt]{report}
usepackage[subpreambles=true]{standalone}
usepackage[ruled,linesnumbered,vlined]{algorithm2e}

usepackage{sectsty}

chapternumberfont{LARGE} 
chaptertitlefont{Huge}
usepackage{import}
usepackage{amsmath,amssymb,amsfonts,amsthm,complexity,tikz,parskip,subcaption}
usepackage{graphicx}
usepackage[nottoc]{tocbibind}
usepackage{setspace}
setcounter{tocdepth}{1}

begin{document}

chapter{Introduction}
    import{./}{import1}
    import{./}{import2}

end{document}

First import:
%!TeX root = import1

documentclass{article}

usepackage{amsthm,enumerate,euscript,tikz}
usepackage[ruled,linesnumbered,vlined]{algorithm2e}
newtheorem{thm}{Theorem}[section]
newtheorem{lem}{Lemma}[section]
newtheorem{cor}{Corollary}[section]

theoremstyle{definition}
newtheorem{dfn}{Definition}

theoremstyle{remark}
newtheorem{rem}{Remark}
begin{document}
    
subsection{Theorem}
begin{thm}
Example theorem
end{thm}
begin{proof}
    Example proof
end{proof}
end{document}

Second import:
%!TeX root = import2

documentclass{article}

usepackage{amsthm,enumerate,euscript,tikz}
usepackage[ruled,linesnumbered,vlined]{algorithm2e}
newtheorem{thm}{Theorem}[section]
newtheorem{lem}{Lemma}[section]
newtheorem{cor}{Corollary}[section]

theoremstyle{definition}
newtheorem{dfn}{Definition}

theoremstyle{remark}
newtheorem{rem}{Remark}
begin{document}
    
subsection{Theorem}
begin{lem}
Example lemma
end{lem}
begin{proof}
    Example proof
end{proof}
end{document}

What causes this error and how can I solve it?

NBur · Accepted Answer

For what I understand, you want compilable subfiles. Thus you provide full preamble in them. The error arises when compiling the main file, because there are multiple definitions with exact same newtheorem. This is due to the subpreambles=true option you pass to standalone.
First option
You can test if the different environments/macros are already defined.
For instance you coded newtheorem{thm}{Theorem}[section], which defines beginthm and endthm. Instead, use
ifdefinedbeginthmelse
newtheorem{thm}{Theorem}[section]
fi

And so on for every newtheorem you defined.
Second option
Add a full preamble in your main file and remove the standalone option.
The drawback being you have to take care of the changes in your various preambles…
Third option
Use the subfiles package. You write only one preamble in your main file, and it is shared with all the subfiles, these ones being compilable alone.
Your main.tex is as follow
documentclass[12pt]{report}
usepackage{amsmath,amssymb,amsfonts,amsthm}
newtheorem{thm}{Theorem}[section]
newtheorem{lem}{Lemma}[section]
newtheorem{cor}{Corollary}[section]

theoremstyle{definition}
newtheorem{dfn}{Definition}

theoremstyle{remark}
newtheorem{rem}{Remark}

% end of shared preamble
usepackage{subfiles}

begin{document}
    
    chapter{Introduction}
    subfile{./import1}
    subfile{./import2}
    
end{document}

And your import.tex files have this structure
documentclass[main]{subfiles}

begin{document}
    
    subsection{Theorem}
    begin{thm}
        Example theorem
    end{thm}
    begin{proof}
        Example proof
    end{proof}
end{document}

EDIT
You can have sub-import. For instance you can code the import1.tex as
documentclass[main]{subfiles}

begin{document}
    
    subsection{Theorem}
    begin{lem}
        Example lemma
    end{lem}
    begin{proof}
        Example proof
    end{proof}
    subfile{import2}
    subfile{import3}
end{document}

but your import3.tex has to share the preamble with the main.tex, not with the import1.tex, ie you have to use documentclass[main]{subfiles} in all your subfiles.

Simon Dispa · Answer

Another way to organize a project and to test partial parts of a document is using input and commenting the (input) of parts you do not want to compile.
The big advantage is that you have  the full  preamble in a single place, so if you change a definition or add a package you do not have to alter all partial files.
Main.tex
documentclass[12pt]{report}
usepackage[subpreambles=true]{standalone}
usepackage[ruled,linesnumbered,vlined]{algorithm2e}

usepackage{sectsty}

chapternumberfont{LARGE} 
chaptertitlefont{Huge}
usepackage{import}
usepackage{amsmath,amssymb,amsfonts,amsthm,complexity,tikz,parskip,subcaption}
usepackage{graphicx}
usepackage[nottoc]{tocbibind}
usepackage{setspace}
setcounter{tocdepth}{1}

usepackage{amsthm,enumerate,euscript,tikz}
usepackage[ruled,linesnumbered,vlined]{algorithm2e}
newtheorem{thm}{Theorem}[section]
newtheorem{lem}{Lemma}[section]
newtheorem{cor}{Corollary}[section]
theoremstyle{definition}
newtheorem{dfn}{Definition}

theoremstyle{remark}
newtheorem{rem}{Remark}

begin{document}

chapter{Introduction}

input{import1c}

input{import2c}

end{document}

import1c.tex
section{Theorem}
begin{thm}
Example theorem
end{thm}
begin{proof}
    Example proof
end{proof}

import2c.tex
section{Theorem}
begin{lem}
Example lemma
end{lem}
begin{proof}
    Example proof
end{proof}

Note
I changed the subsection to section to match the newtheorem definitions thus getting proper numbering.

gernot · Answer

There is the subfiles package intended for such purposes, even though you should try input first as suggested in the other answer, as it is much simpler.
With the subfiles package, you keep the preamble in the main file and load it from the subfiles as well. For details, see the documentation of the subfiles package
% temp.tex
documentclass[12pt]{report}
%usepackage[subpreambles=true]{standalone}
usepackage[ruled,linesnumbered,vlined]{algorithm2e}
usepackage{sectsty}
chapternumberfont{LARGE} 
chaptertitlefont{Huge}

usepackage{amsmath,amssymb,amsfonts,amsthm,complexity,tikz,parskip,subcaption}
newtheorem{thm}{Theorem}[section]
newtheorem{lem}{Lemma}[section]
newtheorem{cor}{Corollary}[section]
theoremstyle{definition}
newtheorem{dfn}{Definition}
theoremstyle{remark}
newtheorem{rem}{Remark}

usepackage{graphicx}
usepackage[nottoc]{tocbibind}
usepackage{setspace}
setcounter{tocdepth}{1}

usepackage{subfiles}%%%%% <<<<< load subfiles package last
begin{document}
....
end{document}

% import1.tex
documentclass[temp]{subfiles}%%%% <<< Reference to the main file with the preamble
begin{document}
subsection{Theorem}
begin{thm}
Example theorem
end{thm}
begin{proof}
    Example proof
end{proof}
end{document}

Note: I'm the maintainer of the subfiles package, but I'm not necessarily advocating its use.

I get "already defined" error when using `amsthm` package with `import`

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