\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{t1\_msafree (TMGjs65YdPH5RJJyVKdhS8RKBx1QLsuWzZ8)}
\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 $ k3\_finseq\_2 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~(k3\_relat\_1~\\
X2~X1)){\unicdbdjdcd}(k1\_funct\_1~(k3\_relat\_1~X2~X1)~X0=k1\_funct\_1~X1~(k1\_funct\_1~\\
X2~X0))))\end{array}
\label{hyp:ehbdcdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_finseq\_2}~{X0}}={{k13\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k1\_relset\_1~X0~X1=k9\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(((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\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~X1){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_partfun1~X3~X1)))))){\unicdbdjdcd}((v1\_relat\_1~(k3\_relat\_1~\\
X2~X3)){\unicdcdcdhd}((v4\_relat\_1~(k3\_relat\_1~X2~X3)~X0){\unicdcdcdhd}((v1\_funct\_1~(k3\_relat\_1~\\
X2~X3)){\unicdcdcdhd}(v1\_partfun1~(k3\_relat\_1~X2~X3)~X0))))\end{array}
\label{hyp:ggdgbdpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k13\_finseq\_1}~{X0}})}}}}}\label{hyp:ggdgbdcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}((v1\_relat\_1~(k6\_finseq\_2~\\
X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k6\_finseq\_2~X0~X1)~(k3\_finseq\_2~X0)){\unicdcdcdhd}((\\
v1\_funct\_1~(k6\_finseq\_2~X0~X1)){\unicdcdcdhd}(v1\_partfun1~(k6\_finseq\_2~X0~\\
X1)~(k3\_finseq\_2~X0)))))\end{array}
\label{hyp:egehpflggdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~(k3\_finseq\_2~X0)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~\\
X2~(k3\_finseq\_2~X0))))){\unicdbdjdcd}((X2=k6\_finseq\_2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(m2\_finseq\_2~X3~X0~(k3\_finseq\_2~X0)){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k4\_card\_3~\\
(k3\_relat\_1~X3~X1)))))\end{array}
\label{hyp:egfdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
(v1\_partfun1~X1~X0){\unicdbdjded}(k1\_relset\_1~X0~X1=X0))\end{array}
\label{hyp:egcdpfahbgchehggfhogbd}
\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\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfngdhbgggchfgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~(k3\_finseq\_2~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~(k3\_finseq\_2~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}((v4\_relat\_1~X3~X1){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_partfun1~X3~X1)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m2\_finseq\_2~X4~X1~(k3\_finseq\_2~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((X5 \in X0){\unicdcdcdhd}(X4=k1\_funct\_1~X2~X5)){\unicdbdjdcd}(k1\_funct\_1~(k3\_relat\_1~X2~(\\
k6\_finseq\_2~X1~X3))~X5=k4\_card\_3~(k3\_relat\_1~X4~X3))))))\end{array}$$
\end{theorem}
\end{document}
