\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{t8\_unialg\_3 (TMGwdTaFXKvPGSDkQDvyWpnvaqBaswu6i8p)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_unialg\_2 : {{\iota}{\unicdbdjdcd}{{\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\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_unialg\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_unialg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_unialg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_unialg\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_unialg\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}\\
((v3\_unialg\_1~X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdcdcdhd}(\\
(\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_unialg\_3~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_unialg\_3~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpffhogjgbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k3\_funct\_2~X0~\\
X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}(k1\_unialg\_3~X0=\\
k9\_unialg\_2~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpffhogjgbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_unialg\_2~\\
X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}\\
((v4\_unialg\_1~X1){\unicdcdcdhd}(l1\_unialg\_1~X1))))))\end{array}
\label{hyp:egehpfngbdpffhogjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_unialg\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpffhogjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v1\_funct\_1~(k3\_unialg\_3~\\
X0)){\unicdcdcdhd}((v1\_funct\_2~(k3\_unialg\_3~X0)~(k1\_unialg\_3~X0)~(k9\_setfam\_1~\\
(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~(k3\_unialg\_3~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k1\_unialg\_3~X0)~(k9\_setfam\_1~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpflgddpffhogjgbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k1\_unialg\_3~X0)){\unicdcdcdhd}(m1\_unialg\_3~(k1\_unialg\_3~X0)~X0))\end{array}
\label{hyp:egehpflgbdpffhogjgbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_struct\_0~X0~X1){\unicdbdjded}\\
(X1 \in u1\_struct\_0~X0))\end{array}
\label{hyp:egfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k1\_unialg\_3~X0)~(k9\_setfam\_1~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_unialg\_3~\\
X0)~(k9\_setfam\_1~(u1\_struct\_0~X0))))))){\unicdbdjdcd}((X1=k3\_unialg\_3~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  (m2\_unialg\_3~X2~X0~(k1\_unialg\_3~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_unialg\_2~X3~X0){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}(k3\_funct\_2~(k1\_unialg\_3~X0)~(k9\_setfam\_1~\\
(u1\_struct\_0~X0))~X1~X2=u1\_struct\_0~X3))))))\end{array}
\label{hyp:egedpffhogjgbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=\\
k9\_unialg\_2~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}((v1\_unialg\_1~X2){\unicdcdcdhd}(m1\_unialg\_2~\\
X2~X0))))\end{array}
\label{hyp:egbdedpffhogjgbgmghgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehidpffhogjgbgmghgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_unialg\_1~\\
X1){\unicdcdcdhd}(m1\_unialg\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((X2 \in k1\_funct\_1~(k3\_unialg\_3~X0)~X1){\unicdbdjded}(r1\_struct\_0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
