[Tex/LaTex] Suggestions for nested proofs

environmentsformattingmacrossymbolstheorems

I would like to write down my lecture notes. The proofs of the theorems in this lecture are usually really big. It usually looks like this:

Theorem 1: Here comes the statement of the Theorem

Proof.

Without loss of generality let us assume…

Claim 1: Statement.

Proof: Blah blah \endOfInnerProofSymbol

Claim 2: Statement.

Proof. Blah blah \endOfInnerProofSymbol

\endOfProofSymbol

So my question is now, how can I make such nested proofs with another QED-symbol than the parent proof (maybe a filled square)?

Best Answer

You can simply define a new environment subproof that mimics the behavior of proof but uses a filled square instead of the default one.

\newenvironment{subproof}[1][\proofname]{%
  \renewcommand{\qedsymbol}{$\blacksquare$}%
  \begin{proof}[#1]%
}{%
  \end{proof}%
}

You can even give it the optional argument as in

\begin{subproof}[Subproof]

so to print "Subproof" instead of "Proof".

MWE (note the \item after the outer proof to let enumerate start on a new line)

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

\newtheorem{theorem}{Theorem}

\newenvironment{subproof}[1][\proofname]{%
  \renewcommand{\qedsymbol}{$\blacksquare$}%
  \begin{proof}[#1]%
}{%
  \end{proof}%
}

\begin{document}
\begin{theorem}
  Here comes the statement of the Theorem
\end{theorem}
\begin{proof}
  \item
  \begin{enumerate}
    \item Without loss of generality let us assume...
    \item Claim 1: Statement.%
    \begin{subproof}[Subproof]
      Blah blah
    \end{subproof}
    \item Claim 2: Statement.%
    \begin{subproof}
      Blah blah
    \end{subproof}
  \end{enumerate} 
\end{proof}
\end{document}

enter image description here

Related Solutions

[Tex/LaTex] amsthm: how to reduce the vertical spacing between theorem and proof

One possibility would be to redefine the proof anvironment as defined in amsthm.sty (the definition uses \topsep6\p@\@plus6\p@\relax, so you could make some changes there). Another approach would be to use the front-end thmtools to define a new theorem-like structure behaving like the standard proof environment, but using the spaceabove key to control the vertical space above it. The following example illustrates this second approach and shows the different spacing for the new prf environment and the standard proof environment:

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

\declaretheorem{theorem} 
\declaretheoremstyle[%
  spaceabove=-6pt,%
  spacebelow=6pt,%
  headfont=\normalfont\itshape,%
  postheadspace=1em,%
  qed=\qedsymbol%
]{mystyle} 
\declaretheorem[name={Proof},style=mystyle,unnumbered,
]{prf}

\begin{document} 

\begin{theorem} 
A really important result.
\end{theorem}
\begin{prf} 
And its proof with less space above.
\end{prf} 
\begin{theorem} 
A really important result.
\end{theorem}
\begin{proof} 
And its proof with too much space above.
\end{proof} 

\end{document}

enter image description here

[Tex/LaTex] How to number subtheorems hierarchically

Update version 2.

\documentclass{scrartcl}   
\usepackage[utf8]{inputenc} 
\usepackage[T1]{fontenc} 

\newtheorem{theorem}{Theorem}[section]
\newtheorem{subtheorem}{Sub-Theorem}[theorem]

 \newenvironment{proof}[1][Proof]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}


\newcommand{\qed}{\nobreak \ifvmode \relax \else
      \ifdim\lastskip<1.5em \hskip-\lastskip
      \hskip1.5em plus0em minus0.5em \fi \nobreak
      \vrule height0.75em width0.5em depth0.25em\fi}

\begin{document}
\section{Introduction}

\begin{theorem} 
  \label{main}
 If $x=2$, $x^3=8$. 
\end{theorem}   

\begin{proof} 

   Let $x=2.$     
  \begin{subtheorem}   
    \label{sub}   
      For all $x$ and all natural numbers $n$, $x^n = x*x*...*x$ (n times).
  \end{subtheorem}


\begin{proof} 
  By induction. \qed
\end{proof} 

(Theorem \ref{main}'s proof continued) by Claim \ref{sub}, $x^3 = 2*2*2 = 8$  .\qed

\end{proof}       
\end{document}

enter image description here

With amsart Now I think (not sure) that your problem comes from Lyx. I think you try to use tag given in the menu but I can't give you a correct answer because I don't know Lyx.Perhaps it's possible to modify the menus, the tags etc. but I don't know ! :(

\documentclass{amsart}   
\usepackage[utf8]{inputenc} 
\usepackage[T1]{fontenc} 

\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}{Lemma}[section]
\newtheorem{cor}{Corollary}[section]
\newtheorem{prop}{Proposition}[section]
\newtheorem{crit}{Criterion}[section]
\newtheorem{alg}{Algorithm}[section]
\theoremstyle{definition}
\newtheorem{defn}{Definition}[section]
\newtheorem{claim}{Claim}[thm] 
\newtheorem{other}{Other}[defn] 


\begin{document}
\section{Introduction}

\begin{defn} 
a new definition that uses this definition 
\end{defn}  

\begin{thm} 
  \label{main}
 If $x=2$, $x^3=8$. 
\end{thm}   

\begin{proof} 

   Let $x=2.$     
  \begin{claim}   
    \label{sub}   
      For all $x$ and all natural numbers $n$, $x^n = x*x*...*x$ (n times).
  \end{claim}


\begin{proof} 
  By induction. 
\end{proof} 

(Theorem \ref{main}'s proof continued) by Claim \ref{sub}, $x^3 = 2*2*2 = 8$.

\end{proof}  

\begin{defn} 
a new definition that uses this definition 
 \begin{other}
     other definition
 \end{other}

\end{defn}        
\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] amsthm: how to reduce the vertical spacing between theorem and proof

[Tex/LaTex] How to number subtheorems hierarchically

Related Question