Theorem-Lemma-Proof environment

Question

Here is the code:

\documentclass{article}


\usepackage{amssymb,latexsym,amsmath} 

\usepackage{ntheorem}
\theorembodyfont{\upshape}
\newtheorem*{theorem}{Theorem:}

\newtheorem*{lemma}{Lemma:}

\newenvironment{proof}{\paragraph{\ Proof:}}{\hfill$\square$}

\RequirePackage{hyperref}
\usepackage[nameinlink]{cleveref}

\begin{document}

\begin{lemma} Here is the statement of the lemma.\label{lemma}
\end{lemma}
\begin{theorem}Here is the statement of the theorem.
\end{theorem}

\begin{proof}This is the proof of the theorem using \Cref{lemma}
\end{proof}
\end{document}

Though I have not numbered the lemma using \newtheorem* while referring to the lemma in the proof of the theorem, Lemma 1 comes up. I want to see Lemma, no numbering after that.

I really appreciate any help you can provide.

Answer 1

I admit I am not sure why you want to use cleveref with this. If you are only using the no-number style then you are probably using the environment only once. And so there's really no need to automatically "detect" reference types! But since you asked for it, here it is.

\documentclass{article}

\usepackage{amssymb,latexsym,amsmath} 

\usepackage{ntheorem}
\usepackage{hyperref}
\usepackage[nameinlink]{cleveref}

\theoremstyle{nonumberplain}   % note 1
\theorembodyfont{\normalfont}
\theoremseparator{:}           % note 2
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}

\theoremsymbol{\ensuremath{\color{lightgray}\blacksquare}}
\newtheorem{proof}{Proof}

\Crefformat{lemma}{#2Lemma#3}   % note 3
\crefformat{lemma}{#2lemma#3}

\begin{document}

\begin{lemma} Here is the statement of the lemma.\label{lemma}
\end{lemma}
\begin{theorem}Here is the statement of the theorem.
\end{theorem}

\begin{proof}This is the proof of the theorem using \Cref{lemma}
\end{proof}
\end{document}

1. Instead of using \newtheorem*, since you are going to need to define the proof environment anyway, and it looks like you are using more or less the same style for all of them, I specified the nonumberplain style.
2. Instead of coding the colon in the theorem name, it is better to use the \theoremseparator to specify it.
3. This is a difference between ntheorem and amsthm. In the latter, theorems created using \newtheorem* get no reference counter, and so cannot be cross referenced. With ntheorem the counter is still there, just suppressed from display. cleveref however does not detect the theorem style at all (in fact, it cares not what the style is). So you have to do it yourself by defining a corresponding \Crefformat and \crefformat. See section 8.2.1 of the cleveref manual for details on how this works.