\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t1\_scmfsa10 (TMJfsstZ3Q3me3BH7UKZJDcZyuo3eLz3bKG)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ k8\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_scmfsa\_2 : {\iota}$ be given.
Let $ k3\_scmfsa\_2 : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_scm\_inst : {\iota}$ be given.
Let $ k2\_ami\_2 : {\iota}$ be given.
Let $ k3\_scmfsa\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}k8\_struct\_0~k1\_scmfsa\_2=k4\_subset\_1~(u1\_struct\_0~k1\_scmfsa\_2)~\\
k2\_scmfsa\_2~k3\_scmfsa\_2\end{array}
\label{hyp:ehbdadadpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_scmfsa\_2}={k2\_scm\_inst}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_ami\_2}={k2\_scm\_inst}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfbgngjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k3\_scmfsa\_2}}~{({{k1\_zfmisc\_1}~{({{u1\_struct\_0}~{k1\_scmfsa\_2}})}})}}\label{hyp:egehpflgddpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k2\_scmfsa\_2}}~{({{k1\_zfmisc\_1}~{({{u1\_struct\_0}~{k1\_scmfsa\_2}})}})}}\label{hyp:egehpflgcdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdbdjdcd}((m1\_scmfsa\_2~\\
X0){\unicdbdjded}(X0 \in k3\_scmfsa\_1))\end{array}
\label{hyp:egfdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdid}(X3 \in X1)))\end{array}
\label{hyp:egddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k3\_scmfsa\_2}={k3\_scmfsa\_1}}\label{hyp:egddpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_ami\_2}~{X0}})}{\unicdbdjded}{({{X0} \in {k2\_ami\_2}})}}}\label{hyp:egbdgdpfbgngjgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfdhdgngggdhbgbdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdbdjdcd}(\preoh (X0 \in \\
k8\_struct\_0~k1\_scmfsa\_2){\unicdcdcdhd}((\preoh (v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(\\
u1\_struct\_0~k1\_scmfsa\_2))){\unicdcdcdhd}(\preoh m1\_scmfsa\_2~X0)))\end{array}$$
\end{theorem}
\end{document}
