How to Make Claims and Proofs start on the same page if possible?

Question

I have a document where sometimes proofs start on a separate page than where their associated claims were stated.

Is it possible to force is so that (unless the statement of the claim is more than one page) the proof will always start on the page where the claim was stated?

Example:

LaTeX Code:

%% LyX 2.2.0dev created this file.  For more info, see http://www.lyx.org/.
%% Do not edit unless you really know what you are doing.
\documentclass[oneside,english,reqno]{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{luainputenc}
\usepackage[a4paper]{geometry}
\geometry{verbose,tmargin=1cm,bmargin=1cm,lmargin=1cm,rmargin=1cm}
\setcounter{secnumdepth}{5}
\usepackage{amsthm}
\usepackage{amssymb}

\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
\swapnumbers
\theoremstyle{plain}
\newtheorem{thm}{\protect\theoremname}[section]
  \theoremstyle{remark}
  \newtheorem{claim}[thm]{\protect\claimname}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
\usepackage[breaklinks,colorlinks=true,linkcolor=blue,
citecolor=blue, urlcolor=blue]{hyperref}
\usepackage{braket}
\usepackage{mathtools}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}%
\DeclarePairedDelimiter\norm{\lVert}{\rVert}%
\let\oldnorm\norm
\def\norm{\@ifstar{\oldnorm}{\oldnorm*}}
\makeatother
\usepackage{amsfonts}
\usepackage{dsfont}
\renewcommand{\vec}[1]{\mathbf{#1}}
\usepackage[scaled=0.88]{beraserif}
\usepackage[scaled=0.85]{berasans}
\usepackage[scaled=0.84]{beramono}
\usepackage[T1]{fontenc}
\usepackage{mathpazo}
\usepackage[T1,small,euler-digits]{eulervm}
%\numberwithin{section}{chapter}
% make boxes around proofs:
%-------------------
\usepackage[framemethod=tikz]{mdframed}
\surroundwithmdframed[
  hidealllines=true,
  leftline=true,
  bottomline=true,
  innertopmargin=0pt,
  skipabove=\dimexpr\topsep+6pt\relax,
  skipbelow=\topsep,
  innerrightmargin=0pt,
]{proof}
%-------------------

\AtBeginDocument{
  \def\labelitemii{\(\circ\)}
  \def\labelitemiv{\(\star\)}
}

\makeatother

\usepackage{babel}
  \providecommand{\claimname}{Claim}
\providecommand{\theoremname}{Theorem}

\begin{document}
A lot of text goes here. A lot of text goes here. A lot of text goes
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A lot of text goes here. A lot of text goes here. A lot of text goes
here. A lot of text goes here. A lot of text goes here. 
\begin{claim}
This is a claim.
\begin{proof}
This is the associated proof. 
\begin{eqnarray*}
\hbar & = & \hbar\\
 & = & \hbar\\
 & = & \hbar\\
 & = & \hbar\\
 & = & \hbar\\
 & = & \hbar\\
 & = & \hbar\\
 & = & \hbar\\
 & = & \hbar
\end{eqnarray*}
\end{proof}
\end{claim}
\end{document}

Answer 1

You can use needspace (but I don't know in the least how you can do this with LyX).

\documentclass[oneside,english,reqno]{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{luainputenc}
\usepackage[a4paper]{geometry}
\geometry{verbose,tmargin=1cm,bmargin=1cm,lmargin=1cm,rmargin=1cm}
\setcounter{secnumdepth}{5}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{needspace}

\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
\swapnumbers
\theoremstyle{plain}
\newtheorem{thm}{\protect\theoremname}[section]
\theoremstyle{remark}
\newtheorem{claimINNER}[thm]{\protect\claimname}
\newenvironment{claim}
 {\par\Needspace{2\baselineskip}\claimINNER}
 {\endclaimINNER}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
\usepackage[breaklinks,colorlinks=true,linkcolor=blue,
citecolor=blue, urlcolor=blue]{hyperref}
\usepackage{braket}
\usepackage{mathtools}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}%
\DeclarePairedDelimiter\norm{\lVert}{\rVert}%
\let\oldnorm\norm
\def\norm{\@ifstar{\oldnorm}{\oldnorm*}}
\makeatother
\usepackage{amsfonts}
\usepackage{dsfont}
\renewcommand{\vec}[1]{\mathbf{#1}}
\usepackage[scaled=0.88]{beraserif}
\usepackage[scaled=0.85]{berasans}
\usepackage[scaled=0.84]{beramono}
\usepackage[T1]{fontenc}
\usepackage{mathpazo}
\usepackage[T1,small,euler-digits]{eulervm}
%\numberwithin{section}{chapter}
% make boxes around proofs:
%-------------------
\usepackage[framemethod=tikz]{mdframed}
\surroundwithmdframed[
  hidealllines=true,
  leftline=true,
  bottomline=true,
  innertopmargin=0pt,
  skipabove=\dimexpr\topsep+6pt\relax,
  skipbelow=\topsep,
  innerrightmargin=0pt,
]{proof}
%-------------------

\AtBeginDocument{
  \def\labelitemii{\(\circ\)}
  \def\labelitemiv{\(\star\)}
}

\makeatother

\usepackage{babel}
  \providecommand{\claimname}{Claim}
\providecommand{\theoremname}{Theorem}

\begin{document}
A lot of text goes here.
A lot of text goes here. A lot of text goes here. A lot of text goes
here. A lot of text goes here. A lot of text goes here. A lot of text
goes here. A lot of text goes here. A lot of text goes here. A lot
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A lot of text goes here. A lot of text goes here. A lot of text goes
here. A lot of text goes here. A lot of text goes here. 
\begin{claim}
This is a claim.
\begin{proof}
This is the associated proof. 
\begin{align*}
A & = B \\
  & = B \\
  & = B \\
  & = B \\
  & = B \\
  & = B \\
  & = B \\
  & = B \\
  & = B 
\end{align*}
\end{proof}
\end{claim}
\end{document}

Answer 2

The answer is in @Christian Hupfer's comment.

You mentioned using lyx, so you need to add ERT before your claim starting a minipage.

\begin{minipage}[]{1 \textwidth}

and an ERT after your proof closing the minipage:

\end{minipage}

Make sure your ERT is always in "standard" environment.

For more information about minipage and it's use look it up in ctan, or take a look at this website

Another way is using samepage: add ERT before claim with

\begin{samepage}

And after proof close with

\end{samepage}

As @Christian Hupfer said the minipage might not put the claim and the proof where you want it, changing the options within the minipage [...] or using samepage might solve your placing problem