\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{t7\_tdgroup (TMXFD1kPijwCYobJixmvEW9YpFtDv8YtF4P)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_tdgroup : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_vectsp\_1 : {\iota}$ be given.
Let $ v8\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}\preoh {\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k1\_vectsp\_1)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k1\_vectsp\_1)){\unicdbdjdcd}(X0=X1))\end{array}
\label{hyp:ehgdpfeheghgchpgfhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v8\_algstr\_0~k1\_vectsp\_1){\unicdcdcdhd}((v13\_algstr\_0~k1\_vectsp\_1){\unicdcdcdhd}((v2\_rlvect\_1~\\
k1\_vectsp\_1){\unicdcdcdhd}((v3\_rlvect\_1~k1\_vectsp\_1){\unicdcdcdhd}(v4\_rlvect\_1~k1\_vectsp\_1))))\end{array}
\label{hyp:ggdgddpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k1\_vectsp\_1}}}})}{\unicdcdcdhd}{({{v8\_algstr\_0}~{k1\_vectsp\_1}})}}\label{hyp:ggdgbdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v8\_algstr\_0~k1\_vectsp\_1){\unicdcdcdhd}((v12\_vectsp\_1~k1\_vectsp\_1){\unicdcdcdhd}(v1\_tdgroup~\\
k1\_vectsp\_1))\end{array}
\label{hyp:ggdgbdpfeheghgchpgfhah}
\end{equation}
Assume the following.
\begin{equation}
{{({{v8\_algstr\_0}~{k1\_vectsp\_1}})}{\unicdcdcdhd}{({{l2\_algstr\_0}~{k1\_vectsp\_1}})}}\label{hyp:egehpflgbdpfghfgdgehdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfeheghgchpgfhah}
$$\begin{array}{c}\preoh {\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v12\_vectsp\_1~X0){\unicdcdcdhd}\\
((v1\_tdgroup~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(X1=X2)))\end{array}$$
\end{theorem}
\end{document}
