\newtheorem*{lemma}{Lemma}
\newtheorem{Lemma}{Lemma}
\newtheorem*{proposition}{Proposition}
\newtheorem{Proposition}{Proposition}
\newtheorem*{theorem}{Theorem}
\newtheorem{Theorem}{Theorem}
\newtheorem*{conjecture}{Conjecture}
\newtheorem{Conjecture}{Conjecture}
\newtheorem*{corollary}{Corollary}
\newtheorem{Corollary}[Lemma]{Corollary}
\theoremstyle{remark}
\newtheorem*{remark}{Remark}
\newtheorem{Remark}{Remark}
\newtheorem*{remarks}{Remarks}
\theoremstyle{definition}
\newtheorem*{definition}{Definition}
\newtheorem{Definition}{Definition}
\newtheorem*{example}{Example}
\newtheorem{Example}{Example}
\newtheorem{Question}{Question}
\newtheorem{Questions}[Question]{Questions}