\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
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\begin{document}
\title{t35\_coh\_sp (TMLSXraP1BENeG8NmWZ4bG8c8gwR59HtKfn)}
\maketitle
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_coh\_sp : {{\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 $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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 .  (v3\_relat\_2~(k6\_partfun1~X0)){\unicdcdcdhd}((v8\_relat\_2~(k6\_partfun1~\\
X0)){\unicdcdcdhd}((v1\_partfun1~(k6\_partfun1~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k6\_partfun1~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))\end{array}
\label{hyp:ehddpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjdcd}(k6\_partfun1~X0 \in k15\_coh\_sp~\\
X1)\end{array}
\label{hyp:ehddbdpfdgpgigpfdhah}
\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 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k4\_relat\_1~X0)){\unicdcdcdhd}((v4\_relat\_1~(k4\_relat\_1~\\
X0)~X0){\unicdcdcdhd}((v1\_funct\_1~(k4\_relat\_1~X0)){\unicdcdcdhd}(v1\_partfun1~(k4\_relat\_1~\\
X0)~X0)))\end{array}
\label{hyp:ggdgbdbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k16\_coh\_sp~X0=ReplSep2~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~(k15\_coh\_sp~X0)))~({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~X0)))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  (v1\_partfun1~X1~\\
X2){\unicdcdcdhd}((v1\_relat\_2~X1){\unicdcdcdhd}((v3\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X2~X2))))))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  k4\_tarski~X1~\\
X2)\end{array}
\label{hyp:egbdidpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k15\_coh\_sp~X0=k3\_tarski~(ReplSep~(toset~({\uniddcgcg} X1 : \iota .  \\
m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))~({\uniddcgcg} X1 : \iota .  True)~({\uniddcgcg} X1 : \\
\iota .  k14\_coh\_sp~X1))\end{array}
\label{hyp:egbdhdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v3\_relat\_2~X0){\unicdcdcdhd}(v8\_relat\_2~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_relat\_2~X0))\end{array}
\label{hyp:dgdgddpfahbgchehggfhogbd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfdgpgigpfdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjdcd}(k4\_tarski~(k6\_partfun1~\\
X0)~X0 \in k16\_coh\_sp~X1)\end{array}$$
\end{theorem}
\end{document}
