\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{t18\_bcialg\_4 (TMQCBjw8ekg7GpAGrU83tC74Lb385EURurp)}
\maketitle
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 $ v5\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_bcialg\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l2\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_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}(r3\_binop\_1~(u1\_struct\_0~X0)~(k4\_struct\_0~\\
X0)~(u1\_bcialg\_4~X0))\end{array}
\label{hyp:ehbdhdpfcgdgjgbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_bcialg\_4~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_bcialg\_4~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_bcialg\_4~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u1\_bcialg\_4~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhbdpfcgdgjgbgmghgpfed}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)~X0))))){\unicdbdjdcd}(({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~X0){\unicdcdcdhd}(r3\_binop\_1~X0~\\
X2~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}((X2=k4\_binop\_1~X0~X1){\unicdbdjded}\\
(r3\_binop\_1~X0~X2~X1))))\end{array}
\label{hyp:egidpfcgjgogpgahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfcgdgjgbgmghgpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v2\_bcialg\_4~X0){\unicdcdcdhd}\\
(l1\_bcialg\_4~X0))))))){\unicdbdjdcd}(k4\_binop\_1~(u1\_struct\_0~X0)~(u1\_bcialg\_4~\\
X0)=k4\_struct\_0~X0)\end{array}$$
\end{theorem}
\end{document}
