\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{t69\_cohsp\_1 (TMSZfBHKzUwEdAGe9PYimL7BxMff4w243aB)}
\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 $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_cohsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_relat\_2 : {{\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 $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\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 .  {\unicdcdadad} X2 .  (r1\_tarski~(k2\_tarski~X1~X2)~(k3\_tarski~\\
X0)){\unicdbdjdcd}((k2\_tarski~X1~X2 \in X0){\unicdcdcdid}(k2\_tarski~X1~X2 \in k13\_cohsp\_1~X0)))\end{array}
\label{hyp:ehgdidpfdgpgigdhahpfbd}
\end{equation}
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 .  {\unicdcdadad} X2 .  \preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}((k2\_tarski~X1~X2 \in X0){\unicdcdcdhd}\\
(k2\_tarski~X1~X2 \in k13\_cohsp\_1~X0)))\end{array}
\label{hyp:ehgdhdpfdgpgigdhahpfbd}
\end{equation}
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}(k3\_tarski~(k13\_cohsp\_1~X0)=k3\_tarski~X0)\end{array}
\label{hyp:ehgdgdpfdgpgigdhahpfbd}
\end{equation}
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 .  ((v1\_partfun1~X1~(k3\_tarski~X0)){\unicdcdcdhd}((v1\_relat\_2~\\
X1){\unicdcdcdhd}((v3\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k3\_tarski~X0)~(k3\_tarski~X0))))))){\unicdbdjdcd}((r2\_relset\_1~(k3\_tarski~\\
X0)~(k3\_tarski~X0)~X1~(k1\_coh\_sp~X0)){\unicdbdjded}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (\\
k4\_tarski~X2~X3 \in X1){\unicdbdjded}(k2\_tarski~X2~X3 \in X0))))\end{array}
\label{hyp:ehfdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_classes1~X1){\unicdcdcdhd}\\
(v1\_coh\_sp~X1))){\unicdbdjdcd}((X0 \in k3\_tarski~X1){\unicdbdjdcd}(k1\_tarski~X0 \in X1))\end{array}
\label{hyp:ehedpfdgpgigpfdhah}
\end{equation}
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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~(k2\_tarski~X0~X1)~\\
X2){\unicdbdjded}((X0 \in X2){\unicdcdcdhd}(X1 \in X2))\end{array}
\label{hyp:ehddcdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k2\_tarski}~{X0}}~{X0}}={{k1\_tarski}~{X0}}}}\label{hyp:ehcdjdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(r2\_relset\_1~X0~X1~X2~X2)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
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}((\preoh v1\_xboole\_0~(k13\_cohsp\_1~X0)){\unicdcdcdhd}((v1\_classes1~(k13\_cohsp\_1~\\
X0)){\unicdcdcdhd}(v1\_coh\_sp~(k13\_cohsp\_1~X0))))\end{array}
\label{hyp:ggdgbdddpfdgpgigdhahpfbd}
\end{equation}
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}((v1\_partfun1~(k1\_coh\_sp~X0)~(k3\_tarski~X0)){\unicdcdcdhd}((v1\_relat\_2~\\
(k1\_coh\_sp~X0)){\unicdcdcdhd}((v3\_relat\_2~(k1\_coh\_sp~X0)){\unicdcdcdhd}(m1\_subset\_1~(\\
k1\_coh\_sp~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_tarski~X0)~(k3\_tarski~\\
X0)))))))\end{array}
\label{hyp:egehpflgbdpfdgpgigpfdhah}
\end{equation}
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}(k13\_cohsp\_1~X0=ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k3\_tarski~X0))))~({\uniddcgcg} X1 : \iota .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdaddd} X3 .  r1\_tarski~(k8\_subset\_1~(k3\_tarski~X0)~X1~X2)~\\
(k1\_tarski~X3)))~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:egcdbdpfdgpgigdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdjdpfdgpgigdhahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_classes1~X0){\unicdcdcdhd}(v1\_coh\_sp~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (k4\_tarski~X1~X2 \in k1\_coh\_sp~(k13\_cohsp\_1~\\
X0)){\unicdbdjded}((X1 \in k3\_tarski~X0){\unicdcdcdhd}((X2 \in k3\_tarski~X0){\unicdcdcdhd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}(k4\_tarski~\\
X1~X2 \in k1\_coh\_sp~X0)))))\end{array}$$
\end{theorem}
\end{document}
