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Is there anyways to have the text totally wrap underneath each item?

\documentclass[a4paper,12pt]{extarticle}
\usepackage[utf8]{inputenc}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{enumitem}

\newtheorem{factinner}{Fact}
\newenvironment{fact}[1]{%
  \renewcommand\thefactinner{#1}%
  \factinner
}{\endfactinner}

\begin{document}
\section{Linear Transformations \& Matrices}
\begin{fact}{1}
\begin{proof}
Proceed by cases.
\begin{enumerate}[leftmargin=*, align=left]
    \item[\textbf{Case 1}] Let $\mathsf{T}$ be linear. Trivial. 

    \item[\textbf{Case 2}] Let $\mathsf{T}(cx + y) = c\mathsf{T}(x) + \mathsf{T}(y)$. To satisfy the first criteria of linearity, let $c =1$. To satisfy the second, let $y = \mathit{0}$. Let $\mathsf{T}(cx + y) = c\mathsf{T}(x) + \mathsf{T}(y)$. To satisfy the first criteria of linearity, let $c =1$. To satisfy the second, let $y = \mathit{0}$. 
\end{enumerate}
\end{proof}
\end{fact}
\end{document}
  • 1
    Unrelated: why are you manually numbering your items? Have to tried label=\textbf{Case \arabic*} and then \item – daleif Jul 29 '19 at 14:40
1

Is this what you want?

\documentclass{article}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{enumitem}

\newtheorem{factinner}{Fact}

\newenvironment{fact}[1]{%
  \renewcommand\thefactinner{#1}%
  \factinner
}{\endfactinner}

\begin{document}

\section{Linear Transformations \& Matrices}

\begin{fact}{1}
\begin{proof}
Proceed by cases.
\begin{enumerate}[label={\textbf{Case \arabic*}}, leftmargin=0pt, itemindent=*]
\item Let $\mathsf{T}$ be linear. Trivial.

\item Let $\mathsf{T}(cx + y) = c\mathsf{T}(x) + \mathsf{T}(y)$. To satisfy
  the first criteria of linearity, let $c =1$. To satisfy the second, let
  $y = \mathit{0}$. Let $\mathsf{T}(cx + y) = c\mathsf{T}(x) + \mathsf{T}(y)$.
  To satisfy the first criteria of linearity, let $c =1$. To satisfy the
  second, let $y = \mathit{0}$.
\end{enumerate}
\end{proof}
\end{fact}

\end{document}

Screenshot

Unrelated: don't you want to have the facts automatically numbered, like this:

\documentclass{article}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{enumitem}

\newtheorem{fact}{Fact}

\begin{document}

\section{Linear Transformations \& Matrices}

\begin{fact}
\begin{proof}
Proceed by cases.
\begin{enumerate}[label={\textbf{Case \arabic*}}, leftmargin=0pt, itemindent=*]
\item Let $\mathsf{T}$ be linear. Trivial.

\item Let $\mathsf{T}(cx + y) = c\mathsf{T}(x) + \mathsf{T}(y)$. To satisfy
  the first criteria of linearity, let $c =1$. To satisfy the second, let
  $y = \mathit{0}$. Let $\mathsf{T}(cx + y) = c\mathsf{T}(x) + \mathsf{T}(y)$.
  To satisfy the first criteria of linearity, let $c =1$. To satisfy the
  second, let $y = \mathit{0}$.
\end{enumerate}
\end{proof}
\end{fact}

\end{document}

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