\documentclass[12pt]{article}

%%%%%%%%%%%%%%%%%%
%\usepackage{amsthm}
%\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage[left=1in,top=1in,right=1in]{geometry}
\usepackage{txfonts}
\usepackage{enumerate}
\usepackage{fancyhdr}

%%%custom definitions
\newcommand{\qedsymbol}{\nobreak
%\begin{flushright}
\fbox{\tiny \textsc{q.e.d.}}
%\end{flushright}
}

%the #1th residual word modulo #2
\newcommand{\residualhk}[2]{
{\!\scriptsize\left[\!\!\!
 \begin{array}{c}
 #1\\
 #2
 \end{array}
\!\!\!\right]}
\!\!\,
}

%the #1th partial derivative of #2 with respect to #3
\newcommand{\pd}[3]{ \frac{\partial^{#1} #2}{\partial {#3}^{#1}} }
%%%

%%%semantic definitions
\newcommand{\intersect}{\cap}
\newcommand{\union}{\cup}
\newcommand{\nonnegative}{\mathbb{N}}
\newcommand{\integer}{\mathbb{Z}}
\newcommand{\rational}{\mathbb{Q}}
\newcommand{\real}{\mathbb{R}}
\newcommand{\complex}{\mathbb{C}}
\renewcommand{\implies}{\Rightarrow}
\newcommand{\assign}{\leftarrow}
\DeclareMathOperator*{\lcm}{lcm}
%%%

%%%local definitions

%%%
%%%%%%%%%%%%%%%%%%

\newtheorem{conj}{Conjecture}
\newtheorem{cor}{Corollary}
\newtheorem{dfn}{Definition}
\newtheorem{lem}{Lemma}
\newtheorem{prop}{Proposition}
\newtheorem{thm}{Theorem}
\newtheorem{ex}{Example}
\newtheorem{alg}{Algorithm}
\newtheorem{proof}{Proof}
\newtheorem{claim}{Claim}

\begin{document}


\end{document}
