\documentclass{article}
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\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\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t40\_coh\_sp (TMZtEMY15Amvop24H9KxsiJJzBaq7rki1mH)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k20\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_coh\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_coh\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 .  {\preoh{{{v1\_xboole\_0}~{({{k20\_coh\_sp}~{X0}})}}}}}\label{hyp:ggdgbdbdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k20\_coh\_sp~X0=ReplSep3~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~(k16\_coh\_sp~X0)))~({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~(k16\_coh\_sp~X0)))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  \\
m1\_subset\_1~X3~(k19\_coh\_sp~X0)))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  ((k17\_coh\_sp~X0~X2=k1\_xboole\_0){\unicdbdjdcd}(k17\_coh\_sp~X0~X1=k1\_xboole\_0)){\unicdcdcdhd}\\
(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k17\_coh\_sp~X0~X1)~(k17\_coh\_sp~\\
X0~X2)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k17\_coh\_sp~\\
X0~X1)~(k17\_coh\_sp~X0~X2)))))){\unicdcdcdhd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  (k4\_tarski~\\
X4~X5 \in k18\_coh\_sp~X0~X1){\unicdbdjdcd}(k4\_tarski~(k1\_funct\_1~X3~X4)~(k1\_funct\_1~\\
X3~X5) \in k18\_coh\_sp~X0~X2))))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  \\
k4\_tarski~(k4\_tarski~X1~X2)~X3)\end{array}
\label{hyp:egcdadpfdgpgigpfdhah}
\end{equation}
\begin{theorem}\label{thm:ehedadpfdgpgigpfdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k20\_coh\_sp~X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  \\
(m1\_subset\_1~X2~(k19\_coh\_sp~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~\\
(k16\_coh\_sp~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(k16\_coh\_sp~X0)){\unicdcdcdhd}\\
((X1=k4\_tarski~(k4\_tarski~X3~X4)~X2){\unicdcdcdhd}(((k17\_coh\_sp~X0~X4=k1\_xboole\_0){\unicdbdjdcd}\\
(k17\_coh\_sp~X0~X3=k1\_xboole\_0)){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(k17\_coh\_sp~X0~X3)~(k17\_coh\_sp~X0~X4)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k17\_coh\_sp~X0~X3)~(k17\_coh\_sp~X0~X4)))))){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  (k4\_tarski~X5~X6 \in k18\_coh\_sp~X0~X3){\unicdbdjdcd}(k4\_tarski~(k1\_funct\_1~\\
X2~X5)~(k1\_funct\_1~X2~X6) \in k18\_coh\_sp~X0~X4))))))))\end{array}$$
\end{theorem}
\end{document}
