\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{t41\_coh\_sp (TMNyMVFwqdfFzXzn1c7CG7xgf4oGWELPJyN)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k16\_coh\_sp : {{\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 $ k17\_coh\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k20\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k19\_coh\_sp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_coh\_sp : {{\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.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X0 \in k19\_coh\_sp~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~(k16\_coh\_sp~X1)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k16\_coh\_sp~X1)){\unicdcdcdhd}\\
(((k17\_coh\_sp~X1~X3=k1\_xboole\_0){\unicdbdjdcd}(k17\_coh\_sp~X1~X2=k1\_xboole\_0)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k17\_coh\_sp~X1~X2)~(k17\_coh\_sp~\\
X1~X3)){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k17\_coh\_sp~\\
X1~X2)~(k17\_coh\_sp~X1~X3)))))))))\end{array}
\label{hyp:ehddjdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_coh\_sp~X0)){\unicdbdjdcd}(k17\_coh\_sp~\\
X0~X1=k2\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdhdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xboole\_0}={{the}~{({{\uniddcgcg} X0 : {\iota} .  {{v1\_xboole\_0}~{X0}}})}}}\label{hyp:egcdpfihcgpgpgmgfgpfad}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k19\_coh\_sp~X0=k3\_tarski~(ReplSep2~(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 .  \\
True)~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  k1\_funct\_2~(k17\_coh\_sp~X0~X1)~(\\
k17\_coh\_sp~X0~X2)))\end{array}
\label{hyp:egbdjdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k16\_coh\_sp~X0=ReplSep2~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~(k15\_coh\_sp~X0)))~({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~X0)))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  (v1\_partfun1~X1~\\
X2){\unicdcdcdhd}((v1\_relat\_2~X1){\unicdcdcdhd}((v3\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X2~X2))))))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  k4\_tarski~X1~\\
X2)\end{array}
\label{hyp:egbdidpfdgpgigpfdhah}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfdgpgigpfdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_coh\_sp~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k16\_coh\_sp~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k17\_coh\_sp~X0~X1)~(k17\_coh\_sp~X0~X2)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k17\_coh\_sp~X0~X1)~(k17\_coh\_sp~X0~\\
X2)))))){\unicdbdjdcd}(({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  (k4\_tarski~X4~X5 \in k18\_coh\_sp~\\
X0~X1){\unicdbdjdcd}(k4\_tarski~(k1\_funct\_1~X3~X4)~(k1\_funct\_1~X3~X5) \in k18\_coh\_sp~\\
X0~X2)){\unicdbdjdcd}(((k17\_coh\_sp~X0~X2=k1\_xboole\_0){\unicdcdcdhd}(k17\_coh\_sp~X0~X1{\unicdcdgdad}k1\_xboole\_0)){\unicdcdcdid}\\
(k4\_tarski~(k4\_tarski~X1~X2)~X3 \in k20\_coh\_sp~X0)))))\end{array}$$
\end{theorem}
\end{document}
