\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{t48\_afvect0 (TMMHEj1E55rvFCZjefqf4ycQp6XDAm1dK77)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_tdgroup : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\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 $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_afvect0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ v1\_afvect0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_afvect0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v8\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_afvect0~X0){\unicdcdcdhd}(l1\_analoaf~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((u1\_struct\_0~\\
(k5\_afvect0~X0~X1)=u1\_struct\_0~X0){\unicdcdcdhd}((u1\_algstr\_0~(k5\_afvect0~\\
X0~X1)=k3\_afvect0~X0~X1){\unicdcdcdhd}(k4\_struct\_0~(k5\_afvect0~X0~X1)=X1))))\end{array}
\label{hyp:ehedcdpfbgggghfgdgehad}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_afvect0~X0){\unicdcdcdhd}\\
(l1\_analoaf~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v8\_algstr\_0~\\
(k5\_afvect0~X0~X1)){\unicdcdcdhd}(v1\_tdgroup~(k5\_afvect0~X0~X1)))\end{array}
\label{hyp:ggdgddpfbgggghfgdgehad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_afvect0~X0){\unicdcdcdhd}\\
(l1\_analoaf~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v8\_algstr\_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))))))\end{array}
\label{hyp:ggdgcdpfbgggghfgdgehad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_analoaf}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgogbgmgpgbggg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_afvect0~X0){\unicdcdcdhd}\\
(l1\_analoaf~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v8\_algstr\_0~\\
(k5\_afvect0~X0~X1)){\unicdcdcdhd}(l2\_algstr\_0~(k5\_afvect0~X0~X1)))\end{array}
\label{hyp:egehpflgfdpfbgggghfgdgehad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}((v7\_struct\_0~X0){\unicdbdjded}({\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}
\label{hyp:egbdadpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{({{v2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{v7\_struct\_0}~{X0}})}})}}}\label{hyp:dgdgbdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_analoaf~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v2\_tdgroup~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v1\_afvect0~X0)))\end{array}
\label{hyp:dgdgbdpfbgggghfgdgehad}
\end{equation}
\begin{theorem}\label{thm:ehedidpfbgggghfgdgehad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v2\_tdgroup~X0){\unicdcdcdhd}(l1\_analoaf~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k5\_afvect0~X0~X1)){\unicdcdcdhd}((\preoh v7\_struct\_0~(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~\\
(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v2\_rlvect\_1~(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~\\
(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v12\_vectsp\_1~\\
(k5\_afvect0~X0~X1)){\unicdcdcdhd}((v1\_tdgroup~(k5\_afvect0~X0~X1)){\unicdcdcdhd}(l2\_algstr\_0~\\
(k5\_afvect0~X0~X1)))))))))))\end{array}$$
\end{theorem}
\end{document}
