\documentclass{article}
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\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t46\_coh\_sp (TMQEFfqJ3fo5B8WYmh7BHoPqk1rqbsNmZua)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k16\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k23\_coh\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_coh\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k21\_coh\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k22\_coh\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k20\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k2\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X1}}}}\label{hyp:chegcdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k1\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X0}}}}\label{hyp:chegbdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_coh\_sp~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k23\_coh\_sp~X0~X1)~(k20\_coh\_sp~X0))\end{array}
\label{hyp:egehpflgcdddpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_coh\_sp~X0)){\unicdbdjdcd}(k23\_coh\_sp~\\
X0~X1=k4\_tarski~(k4\_tarski~X1~X1)~(k6\_partfun1~(k17\_coh\_sp~X0~X1)))\end{array}
\label{hyp:egcdddpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k20\_coh\_sp~X0)){\unicdbdjdcd}(k22\_coh\_sp~\\
X0~X1=k2\_xtuple\_0~(k1\_xtuple\_0~X1))\end{array}
\label{hyp:egcdcdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k20\_coh\_sp~X0)){\unicdbdjdcd}(k21\_coh\_sp~\\
X0~X1=k1\_xtuple\_0~(k1\_xtuple\_0~X1))\end{array}
\label{hyp:egcdbdpfdgpgigpfdhah}
\end{equation}
\begin{theorem}\label{thm:ehedgdpfdgpgigpfdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_coh\_sp~X0)){\unicdbdjdcd}((k2\_xtuple\_0~\\
(k23\_coh\_sp~X0~X1)=k6\_partfun1~(k17\_coh\_sp~X0~X1)){\unicdcdcdhd}((k21\_coh\_sp~\\
X0~(k23\_coh\_sp~X0~X1)=X1){\unicdcdcdhd}(k22\_coh\_sp~X0~(k23\_coh\_sp~X0~X1)=X1)))\end{array}$$
\end{theorem}
\end{document}
