\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{t35\_tex\_1 (TMcc5eUGbBv3EVcTrNbUHN6fbKUwXqCNA3a)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_tdlat\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_tex\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_tdlat\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k4\_xboole\_0~X0~X1=k1\_xboole\_0){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddhdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k6\_subset\_1~X0~(k6\_domain\_1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_tex\_1~X0~X1)))){\unicdbdjdcd}\\
(((X2=k6\_domain\_1~X0~X1){\unicdbdjdcd}((v4\_pre\_topc~X2~(k3\_tex\_1~X0~X1)){\unicdcdcdhd}(\\
v2\_tops\_1~X2~(k3\_tex\_1~X0~X1)))){\unicdcdcdhd}(((v4\_pre\_topc~X2~(k3\_tex\_1~X0~\\
X1)){\unicdcdcdhd}(v2\_tops\_1~X2~(k3\_tex\_1~X0~X1))){\unicdbdjdcd}((v1\_xboole\_0~X2){\unicdcdcdid}(X2=\\
k6\_domain\_1~X0~X1)))))))\end{array}
\label{hyp:ehcdbdpfehfgihpfbd}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k6\_domain\_1~X0~X1=k1\_tarski~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_pre\_topc~X0~X1=g1\_pre\_topc~\\
X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(\preoh v2\_struct\_0~(k3\_tex\_1~X0~X1))\end{array}
\label{hyp:ggdggdpfehfgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_zfmisc\_1~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdggdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}((v1\_pre\_topc~(k3\_tex\_1~\\
X0~X1)){\unicdcdcdhd}(v2\_pre\_topc~(k3\_tex\_1~X0~X1)))\end{array}
\label{hyp:ggdgfdpfehfgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_tarski}~{X0}})}}}}}\label{hyp:ggdgcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{v3\_card\_1}~{({{k1\_tarski}~{X0}})}}~{np\_\_1}}}\label{hyp:ggdgbdddpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_pre\_topc~X0)~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpffhbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(k6\_domain\_1~X0~X1)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflggdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(l1\_pre\_topc~(k3\_tex\_1~\\
X0~X1))\end{array}
\label{hyp:egehpflgddpfehfgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((v3\_tdlat\_3~X0){\unicdbdjded}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(\preoh v3\_tops\_1~X1~X0)))\end{array}
\label{hyp:eggdpfehfgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(k3\_tex\_1~X0~X1=g1\_pre\_topc~\\
X0~(k7\_subset\_1~(k1\_zfmisc\_1~X0)~(k9\_setfam\_1~X0)~(ReplSep~(toset~\\
({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~(k1\_zfmisc\_1~X0)))~({\uniddcgcg} X2 : \iota .  (\\
X1 \in X2){\unicdcdcdhd}(X2{\unicdcdgdad}X0))~({\uniddcgcg} X2 : \iota .  X2))))\end{array}
\label{hyp:egedpfehfgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{v3\_card\_1}~{X0}}~{np\_\_1}})}{\unicdbdjdcd}{({{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdcdcdhd}{({{v1\_zfmisc\_1}~{X0}})}})}}}\label{hyp:dgdgjdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((v4\_pre\_topc~\\
X1~X0){\unicdcdcdhd}(v2\_tops\_1~X1~X0)){\unicdbdjdcd}(v3\_tops\_1~X1~X0)))\end{array}
\label{hyp:dgdgfdpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_zfmisc\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_zfmisc\_1~X1))\end{array}
\label{hyp:dgdgfdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~\\
X0){\unicdcdcdhd}(\preoh v1\_tdlat\_3~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}\\
(v2\_pre\_topc~X0))))\end{array}
\label{hyp:dgdgddpfehfgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{({{v1\_tdlat\_3}~{X0}})}{\unicdbdjdcd}{({{v3\_tdlat\_3}~{X0}})}})}}}\label{hyp:dgdgddpfehegmgbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v1\_pre\_topc~X0){\unicdbdjdcd}(X0=g1\_pre\_topc~\\
(u1\_struct\_0~X0)~(u1\_pre\_topc~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfahchfgpfehpgahdg}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfehfgihpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
((\preoh (\preoh v1\_xboole\_0~(k6\_subset\_1~X0~(k6\_domain\_1~X0~X1))){\unicdcdcdhd}(v3\_tdlat\_3~\\
(k3\_tex\_1~X0~X1))){\unicdcdcdhd}(\preoh (\preoh v3\_tdlat\_3~(k3\_tex\_1~X0~X1)){\unicdcdcdhd}(v1\_xboole\_0~\\
(k6\_subset\_1~X0~(k6\_domain\_1~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
