\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\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t18\_coh\_sp (TMVA3kCvV2zVfCFzAbQGmdpHvdfzJr3ssTR)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_tarski : {{\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 $ k2\_tarski : {{\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}~{({{k5\_coh\_sp}~{X0}})}}}}}\label{hyp:ggdgddpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k5\_coh\_sp~X0=ReplSep3~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~(k3\_coh\_sp~X0)))~({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~(k3\_coh\_sp~X0)))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  \\
m1\_subset\_1~X3~(k4\_coh\_sp~X0)))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  ((k3\_tarski~X2=k1\_xboole\_0){\unicdbdjdcd}(k3\_tarski~X1=k1\_xboole\_0)){\unicdcdcdhd}\\
(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k3\_tarski~X1)~(k3\_tarski~X2)){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_tarski~X1)~(k3\_tarski~\\
X2)))))){\unicdcdcdhd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  (k2\_tarski~X4~X5 \in X1){\unicdbdjdcd}(k2\_tarski~\\
(k1\_funct\_1~X3~X4)~(k1\_funct\_1~X3~X5) \in X2))))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  {\uniddcgcg} X3 : \iota .  k4\_tarski~(k4\_tarski~X1~X2)~X3)\end{array}
\label{hyp:eggdpfdgpgigpfdhah}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfdgpgigpfdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k5\_coh\_sp~X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  \\
(m1\_subset\_1~X2~(k4\_coh\_sp~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(\\
k3\_coh\_sp~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(k3\_coh\_sp~X0)){\unicdcdcdhd}(\\
(X1=k4\_tarski~(k4\_tarski~X3~X4)~X2){\unicdcdcdhd}(((k3\_tarski~X4=k1\_xboole\_0){\unicdbdjdcd}\\
(k3\_tarski~X3=k1\_xboole\_0)){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(k3\_tarski~X3)~(k3\_tarski~X4)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_tarski~X3)~(k3\_tarski~X4)))))){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  (k2\_tarski~X5~X6 \in X3){\unicdbdjdcd}(k2\_tarski~(k1\_funct\_1~X2~X5)~\\
(k1\_funct\_1~X2~X6) \in X4))))))))\end{array}$$
\end{theorem}
\end{document}
