Some starter latex code for a proof based class

example.tex

\documentclass[11pt]{article}
\usepackage[dvipsnames]{xcolor}        % write text in pretty colors
\usepackage[hidelinks]{hyperref}   % makes section links, bibliography links clickable
\usepackage{bm}
\usepackage{booktabs}  % for pretty tables
\usepackage{enumerate}
\usepackage{fullpage}
\usepackage{graphicx}   % include images
\usepackage{hyperref}
\usepackage{listings}   % include the contents of code files (avoids version issues!)
\usepackage{mathpazo} % a better font than the default, according to some
\usepackage{mathtools,amssymb,amsthm}
\usepackage{multicol}
\usepackage{tikzsymbols}
\usepackage{wrapfig}    % wrap text at the side of a smaller figure (don't bother doing this for your own figures)
\graphicspath{ {./images/} }
\hypersetup{
	colorlinks=true,
	linkcolor=blue,
	filecolor=magenta,
	urlcolor=blue,
	pdfpagemode=FullScreen,
}
\usepackage[ruled,vlined,linesnumbered]{algorithm2e}
\newtheorem{theorem}{Theorem}
\newtheorem{prop}{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\renewcommand\qedsymbol{$\Laughey$}
\title{Problem Set #}
\author{Name}
\begin{document}
\maketitle{}

\begin{prop}
prop
\end{prop}
\begin{proof}
We proceed by induction. 
\newline{}
\textit{Base Case:} base
\newline{}
\textit{Induction Step:} step
\begin{align*}
1 = 2\
\end{align*}
Thus, through the principle of mathematical induction, we can prove the following:
\end{proof}

\begin{algorithm}[H]
\KwIn{input}
\KwOut{output}
\tcc{comment}
\vspace{5mm}
\SetAlgoLined{}
some code here\;
$x \leftarrow 0$\;
$y \leftarrow 0$\;
\uIf{$ x > 5$} {
    x is greater than 5\;
}
\uElse {
    x is less than or equal to 5\;
}
\ForEach{y in 0..5} {
    $y \leftarrow y + 1$\;
}
\For{$y$ in $0..5$} {
    $y \leftarrow y - 1$\;
}
\While{$x > 5$} {
    $x \leftarrow x - 1$\;
}
\Return Return something here\;
\caption{what}
\end{algorithm}

\end{document}