\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{t9\_instalg1 (TMRnvE1XWwxWBYvLRF1Wcy3nWV4vDmEAcNc)}
\maketitle
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_pua2mss1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((r1\_tarski~\\
(k10\_xtuple\_0~X1)~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k9\_xtuple\_0~\\
X1)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_xtuple\_0~\\
X1)~X0))))))\end{array}
\label{hyp:ehcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_msualg\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}((r3\_pua2mss1~X0~X1~X2~X3){\unicdbdjded}((k9\_xtuple\_0~\\
X2=u1\_struct\_0~X0){\unicdcdcdhd}((k9\_xtuple\_0~X3=u4\_struct\_0~X0){\unicdcdcdhd}((r1\_tarski~\\
(k10\_xtuple\_0~X2)~(u1\_struct\_0~X1)){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~\\
X3)~(u4\_struct\_0~X1)){\unicdcdcdhd}((k3\_relat\_1~(u2\_msualg\_1~X0)~X2=k3\_relat\_1~\\
X3~(u2\_msualg\_1~X1)){\unicdcdcdhd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}\\
(v1\_funct\_1~X5)){\unicdbdjdcd}(((X4 \in u4\_struct\_0~X0){\unicdcdcdhd}(X5=k1\_funct\_1~(u1\_msualg\_1~\\
X0)~X4)){\unicdbdjdcd}(k3\_relat\_1~X5~X2=k1\_funct\_1~(u1\_msualg\_1~X1)~(k1\_funct\_1~\\
X3~X4)))))))))))))\end{array}
\label{hyp:egbdcdpfahfhbgcdngdhdhbd}
\end{equation}
\begin{theorem}\label{thm:ehjdpfjgogdhehbgmghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_msualg\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}((r3\_pua2mss1~X0~X1~X2~X3){\unicdbdjdcd}(((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u4\_struct\_0~X0)~(u4\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(u4\_struct\_0~X1)))))))))))\end{array}$$
\end{theorem}
\end{document}
