\documentclass{article}
\newtheorem{axiom}{Axiom}
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\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t50\_funcop\_1 (TMQawXn41f9gq2kV8fieoB3C5PFeF9SpXZM)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k9\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k4\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}\\
(v1\_funct\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  k3\_relat\_1~X1~(k4\_funcop\_1~X2~X0~\\
X3)=k4\_funcop\_1~X2~(k3\_relat\_1~X1~X0)~X3)))\end{array}
\label{hyp:ehcdjdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~(k4\_relset\_1~X0~X0~X0~\\
X1~(k6\_partfun1~X0)~X2)~X2){\unicdcdcdhd}(r2\_relset\_1~X0~X1~(k4\_relset\_1~X0~X1~\\
X1~X1~X2~(k6\_partfun1~X1))~X2))\end{array}
\label{hyp:ehbdhdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))){\unicdbdjdcd}(r2\_funct\_2~X0~X1~X2~X2)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchcdpfggfhogdgehpfcd}
\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~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))))){\unicdcdcdhd}(m1\_subset\_1~X4~X0)))){\unicdbdjdcd}\\
(k9\_funcop\_1~X0~X1~X2~X3~X4=k4\_funcop\_1~X2~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))){\unicdbdjdcd}(k4\_relset\_1~X0~X1~X2~X3~\\
X4~X5=k3\_relat\_1~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~X3))))){\unicdbdjdcd}(k1\_partfun1~X0~X1~X2~X3~X4~X5=k3\_relat\_1~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k2\_zfmisc\_1}~{X0}}~{X1}})}}}}\label{hyp:ggdggdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k4\_relat\_1~X0)){\unicdcdcdhd}((v4\_relat\_1~(k4\_relat\_1~\\
X0)~X0){\unicdcdcdhd}((v1\_funct\_1~(k4\_relat\_1~X0)){\unicdcdcdhd}(v1\_partfun1~(k4\_relat\_1~\\
X0)~X0)))\end{array}
\label{hyp:ggdgbdbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))))){\unicdcdcdhd}(m1\_subset\_1~X4~X0)))){\unicdbdjdcd}\\
((v1\_funct\_1~(k9\_funcop\_1~X0~X1~X2~X3~X4)){\unicdcdcdhd}((v1\_funct\_2~(k9\_funcop\_1~\\
X0~X1~X2~X3~X4)~X1~X0){\unicdcdcdhd}(m1\_subset\_1~(k9\_funcop\_1~X0~X1~X2~X3~X4)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X0)))))\end{array}
\label{hyp:egehpflgjdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_partfun1~(k6\_partfun1~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k6\_partfun1~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))\end{array}
\label{hyp:egehpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))){\unicdbdjdcd}(m1\_subset\_1~(k4\_relset\_1~\\
X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X3)))\end{array}
\label{hyp:egehpflgedpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_relat\_1}~{({{k4\_relat\_1}~{X0}})}}}\label{hyp:egehpflgedpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_relat\_1~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v1\_partfun1~X2~X0){\unicdbdjdcd}(v1\_funct\_2~X2~X0~X1))\end{array}
\label{hyp:dgdgbdpfggfhogdgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehfdadpfggfhogdgpgahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)~X0))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~X0){\unicdbdjdcd}(r2\_funct\_2~X1~X0~(k1\_partfun1~X1~X0~X0~X0~X3~\\
(k9\_funcop\_1~X0~X0~X2~(k6\_partfun1~X0)~X4))~(k9\_funcop\_1~X0~X1~X2~\\
X3~X4))))))\end{array}$$
\end{theorem}
\end{document}
