\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{t38\_cohsp\_1 (TMb7pJVQvohFrFVb9PRKGYixe6RKmzprU25)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_coh\_sp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\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 $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ v9\_cohsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_cohsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_cohsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_classes1~X0){\unicdcdcdhd}(v1\_coh\_sp~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_classes1~X1){\unicdcdcdhd}(v1\_coh\_sp~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~(k3\_tarski~X1)))){\unicdbdjdcd}(\preoh ({\unicdcdadad} X3 .  (X3 \in X2){\unicdbdjdcd}(v1\_finset\_1~(k1\_xtuple\_0~\\
X3))){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~X0){\unicdbdjdcd}((k2\_xboole\_0~X3~X4 \in X0){\unicdbdjdcd}({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  ((k4\_tarski~\\
X3~X5 \in X2){\unicdcdcdhd}(k4\_tarski~X4~X6 \in X2)){\unicdbdjdcd}(k2\_tarski~X5~X6 \in X1))))){\unicdcdcdhd}(({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}((k2\_xboole\_0~\\
X3~X4 \in X0){\unicdbdjdcd}({\unicdcdadad} X5 .  ((k4\_tarski~X3~X5 \in X2){\unicdcdcdhd}(k4\_tarski~X4~X5 \in \\
X2)){\unicdbdjdcd}(X3=X4))))){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~X0~X1){\unicdcdcdhd}((v9\_cohsp\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))))){\unicdbdjdcd}(\preoh (X2=k8\_cohsp\_1~X0~X1~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~X0){\unicdbdjdcd}(k3\_funct\_2~X0~X1~X3~X4=k7\_relat\_1~X2~(k3\_cohsp\_1~X0~X4))))))))))\end{array}
\label{hyp:mgfdjdpfdgpgigdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfdgpgigdhahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_classes1~X0){\unicdcdcdhd}(v1\_coh\_sp~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_classes1~X1){\unicdcdcdhd}(v1\_coh\_sp~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~(k3\_tarski~X1)))){\unicdbdjdcd}(\preoh ({\unicdcdadad} X3 .  (X3 \in X2){\unicdbdjdcd}(v1\_finset\_1~(k1\_xtuple\_0~\\
X3))){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~X0){\unicdbdjdcd}((k2\_xboole\_0~X3~X4 \in X0){\unicdbdjdcd}({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  ((k4\_tarski~\\
X3~X5 \in X2){\unicdcdcdhd}(k4\_tarski~X4~X6 \in X2)){\unicdbdjdcd}(k2\_tarski~X5~X6 \in X1))))){\unicdcdcdhd}(({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}((k2\_xboole\_0~\\
X3~X4 \in X0){\unicdbdjdcd}({\unicdcdadad} X5 .  ((k4\_tarski~X3~X5 \in X2){\unicdcdcdhd}(k4\_tarski~X4~X5 \in \\
X2)){\unicdbdjdcd}(X3=X4))))){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~X0~X1){\unicdcdcdhd}((v9\_cohsp\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))))){\unicdbdjdcd}(X2{\unicdcdgdad}k8\_cohsp\_1~X0~X1~X3)))))))\end{array}$$
\end{theorem}
\end{document}
