\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{l71\_bcialg\_4 (TMMtpu4NQEVT9K6y6t92bSnyV96DKun9Hab)}
\maketitle
Let $ v5\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_bcialg\_4 : {\iota}$ be given.
Let $ v6\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_bcialg\_4 : {{\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\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v8\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v2\_bcialg\_4~X0){\unicdcdcdhd}\\
(l1\_bcialg\_4~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((k1\_bcialg\_4~X0~(k4\_struct\_0~X0)~X1=X1){\unicdcdcdhd}(k1\_bcialg\_4~X0~\\
X1~(k4\_struct\_0~X0)=X1)))\end{array}
\label{hyp:ehjdpfcgdgjgbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v3\_bcialg\_1~k2\_bcialg\_4){\unicdcdcdhd}((v4\_bcialg\_1~k2\_bcialg\_4){\unicdcdcdhd}((v5\_bcialg\_1~\\
k2\_bcialg\_4){\unicdcdcdhd}((v7\_bcialg\_1~k2\_bcialg\_4){\unicdcdcdhd}((v8\_bcialg\_1~k2\_bcialg\_4){\unicdcdcdhd}\\
(v2\_bcialg\_4~k2\_bcialg\_4)))))\end{array}
\label{hyp:mgedpfcgdgjgbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v13\_struct\_0}~{k2\_bcialg\_4}}~{np\_\_1}})}{\unicdcdcdhd}{({{v1\_bcialg\_4}~{k2\_bcialg\_4}})}}\label{hyp:ggdgbdpfcgdgjgbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_bcialg\_4}~{X0}})}{\unicdbdjdcd}{({{({{l2\_bcialg\_1}~{X0}})}{\unicdcdcdhd}{({{l2\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgbdpfcgdgjgbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_struct\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k4\_struct\_0~X0)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflgedpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{l1\_bcialg\_4}~{k2\_bcialg\_4}}\label{hyp:egehpflgcdpfcgdgjgbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)){\unicdbdjdcd}((v5\_bcialg\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_bcialg\_1~\\
X0~X1~X1=k4\_struct\_0~X0)))\end{array}
\label{hyp:egfdpfcgdgjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_bcialg\_4~X0)){\unicdbdjdcd}((v7\_bcialg\_4~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_bcialg\_4~X0~(k1\_bcialg\_1~\\
X0~X1~X2)~X2=k1\_bcialg\_4~X0~X1~X2))))\end{array}
\label{hyp:egbdedpfcgdgjgbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_bcialg\_4~X0)){\unicdbdjdcd}((v6\_bcialg\_4~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_bcialg\_4~X0~X1~X2=k1\_bcialg\_4~\\
X0~X2~X1))))\end{array}
\label{hyp:egbdddpfcgdgjgbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_bcialg\_4~X0)){\unicdbdjdcd}((v5\_bcialg\_4~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_bcialg\_4~\\
X0~X1~X1=X1)))\end{array}
\label{hyp:egbdcdpfcgdgjgbgmghgpfed}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}((v13\_struct\_0~X0~np\_\_1){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(v7\_struct\_0~X0)))\end{array}
\label{hyp:dgdgbdbdpfdhehchfhdgehpfad}
\end{equation}
\begin{theorem}\label{thm:mghdbdpfcgdgjgbgmghgpfed}
$$\begin{array}{c}(v5\_bcialg\_4~k2\_bcialg\_4){\unicdcdcdhd}((v6\_bcialg\_4~k2\_bcialg\_4){\unicdcdcdhd}((v7\_bcialg\_4~\\
k2\_bcialg\_4){\unicdcdcdhd}((v5\_bcialg\_1~k2\_bcialg\_4){\unicdcdcdhd}(v2\_bcialg\_4~k2\_bcialg\_4))))\end{array}$$
\end{theorem}
\end{document}
