\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\_conlat\_1 (TMXLoEh1AvwftaV5G3H4CY65ExxYDUuRoGr)}
\maketitle
Let $ v1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\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 $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{\unicdcdadad} X2 .  {{({{X2} \in {X0}})}{\unicdbdjded}{({{X2} \in {X1}})}}})}{\unicdbdjdcd}{({{X0}={X1}})}}}}\label{hyp:ehbdpfehbgchdhlgjg}
\end{equation}
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}
{{\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 .  {\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}(v1\_xboole\_0~\\
X1)\end{array}
\label{hyp:chdgcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l5\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_zfmisc\_1}~{X0}})}}}}}\label{hyp:ggdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_conlat\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k2\_conlat\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k2\_conlat\_1~X0)~(k9\_setfam\_1~\\
(u4\_struct\_0~X0))~(k9\_setfam\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
(k2\_conlat\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_setfam\_1~(u4\_struct\_0~\\
X0))~(k9\_setfam\_1~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpflgcdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k9\_setfam\_1~(u4\_struct\_0~X0))~\\
(k9\_setfam\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k9\_setfam\_1~(u4\_struct\_0~X0))~(k9\_setfam\_1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}((X1=k2\_conlat\_1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(u4\_struct\_0~X0))){\unicdbdjdcd}(k3\_funct\_2~(k1\_zfmisc\_1~(u4\_struct\_0~\\
X0))~(k9\_setfam\_1~(u1\_struct\_0~X0))~X1~X2=ReplSep~(toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~(u1\_struct\_0~X0)))~({\uniddcgcg} X3 : \iota .  {\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u4\_struct\_0~X0)){\unicdbdjdcd}((X4 \in X2){\unicdbdjdcd}(r1\_conlat\_1~X0~X3~\\
X4)))~({\uniddcgcg} X3 : \iota .  X3)))))\end{array}
\label{hyp:egedpfdgpgogmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfdgpgogmgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}(k1\_funct\_1~\\
(k2\_conlat\_1~X0)~k1\_xboole\_0=u1\_struct\_0~X0)\end{array}$$
\end{theorem}
\end{document}
