\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{t43\_coh\_sp (TMG6hRw2MhUKmhpGu8cbhyeuG28oBLvfcU6)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k20\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_coh\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k22\_coh\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k21\_coh\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k4\_tarski : {{\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 $ k19\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k20\_coh\_sp~X0)){\unicdbdjdcd}(X1=k4\_tarski~\\
(k4\_tarski~(k21\_coh\_sp~X0~X1)~(k22\_coh\_sp~X0~X1))~(k2\_xtuple\_0~\\
X1))\end{array}
\label{hyp:ehedcdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\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}
\label{hyp:ehedadpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_coh\_sp~X0)){\unicdbdjdcd}(k18\_coh\_sp~\\
X0~X1=k1\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdidpfdgpgigpfdhah}
\end{equation}
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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(k4\_tarski~(k4\_tarski~X0~X2)~X4=k4\_tarski~(k4\_tarski~X1~X3)~X5){\unicdbdjdcd}\\
((X0=X1){\unicdcdcdhd}(X2=X3))\end{array}
\label{hyp:mgbdadpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k20\_coh\_sp~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
(k2\_xtuple\_0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k2\_xtuple\_0~X1)))\end{array}
\label{hyp:ggdgbdcdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k20\_coh\_sp~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k22\_coh\_sp~X0~X1)~(k16\_coh\_sp~X0))\end{array}
\label{hyp:egehpflgcdcdpfdgpgigpfdhah}
\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}
\begin{theorem}\label{thm:ehedddpfdgpgigpfdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k20\_coh\_sp~X0)){\unicdbdjdcd}((\preoh (k17\_coh\_sp~\\
X0~(k22\_coh\_sp~X0~X1)=k1\_xboole\_0){\unicdcdcdhd}(k17\_coh\_sp~X0~(k21\_coh\_sp~\\
X0~X1){\unicdcdgdad}k1\_xboole\_0)){\unicdcdcdhd}(((v1\_funct\_1~(k2\_xtuple\_0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k2\_xtuple\_0~X1)~(k17\_coh\_sp~X0~(k21\_coh\_sp~X0~X1))~(k17\_coh\_sp~\\
X0~(k22\_coh\_sp~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~(k2\_xtuple\_0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k17\_coh\_sp~X0~(k21\_coh\_sp~X0~X1))~(k17\_coh\_sp~X0~\\
(k22\_coh\_sp~X0~X1))))))){\unicdcdcdhd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X2~\\
X3 \in k18\_coh\_sp~X0~(k21\_coh\_sp~X0~X1)){\unicdbdjdcd}(k4\_tarski~(k1\_funct\_1~(\\
k2\_xtuple\_0~X1)~X2)~(k1\_funct\_1~(k2\_xtuple\_0~X1)~X3) \in k18\_coh\_sp~\\
X0~(k22\_coh\_sp~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
