\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{t51\_afvect0 (TMJzv9XWhdzrAWNd5Hn8ko6dVxz3qDnViKQ)}
\maketitle
Let $ v1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_tdgroup : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ k2\_tdgroup : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_afvect0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v8\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_analoaf~X0){\unicdcdcdhd}((v2\_tdgroup~\\
X0){\unicdcdcdhd}(l1\_analoaf~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(X0=k2\_tdgroup~(k5\_afvect0~X0~X1)))\end{array}
\label{hyp:ehfdadpfbgggghfgdgehad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v2\_tdgroup~X0){\unicdcdcdhd}(l1\_analoaf~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k5\_afvect0~X0~X1)){\unicdcdcdhd}((\preoh v7\_struct\_0~(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~\\
(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v2\_rlvect\_1~(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~\\
(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v12\_vectsp\_1~\\
(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v1\_tdgroup~(k5\_afvect0~X0~X1)){\unicdcdcdhd}(l2\_algstr\_0~\\
(k5\_afvect0~X0~X1)))))))))))\end{array}
\label{hyp:ehedidpfbgggghfgdgehad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_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}\\
((\preoh v7\_struct\_0~(k2\_tdgroup~X0)){\unicdcdcdhd}((v1\_analoaf~(k2\_tdgroup~X0)){\unicdcdcdhd}\\
(v2\_tdgroup~(k2\_tdgroup~X0))))\end{array}
\label{hyp:ggdggdpfbgggghfgdgehad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v2\_tdgroup~X0){\unicdcdcdhd}\\
(l1\_analoaf~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v8\_algstr\_0~\\
(k5\_afvect0~X0~X1)){\unicdcdcdhd}(v12\_vectsp\_1~(k5\_afvect0~X0~X1)))\end{array}
\label{hyp:ggdgedpfbgggghfgdgehad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdaddd} X1 .  {{{m1\_subset\_1}~{X1}}~{X0}}}}\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdbdpfbgggghfgdgehad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_analoaf~X0){\unicdcdcdhd}(l1\_analoaf~X0)){\unicdbdjdcd}(((\preoh v7\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_tdgroup~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjded}({\unicdcdaddd} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}\\
((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v12\_vectsp\_1~X1){\unicdcdcdhd}((v1\_tdgroup~\\
X1){\unicdcdcdhd}(l2\_algstr\_0~X1))))))))){\unicdcdcdhd}(X0=k2\_tdgroup~X1)))\end{array}$$
\end{theorem}
\end{document}
