\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{t3\_mesfunc5 (TMSsXzz1d364sk6bo4v2pm7zidaUi1bNvs1)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_extreal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_supinf\_1 : {\iota}$ be given.
Let $ k2\_supinf\_1 : {\iota}$ be given.
Let $ k2\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Let $ k3\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~(k2\_supinf\_2~\\
(k3\_extreal1~X0))~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~(k3\_extreal1~X0)))\end{array}
\label{hyp:ehjdpffgihehchfgbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh (X0=k1\_xxreal\_0){\unicdcdcdhd}(X1=k1\_xxreal\_0)){\unicdcdcdhd}\\
((\preoh (X0=k2\_xxreal\_0){\unicdcdcdhd}(X1=k2\_xxreal\_0)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X2~(\\
k3\_xxreal\_3~X0~X1)){\unicdcdcdhd}(\preoh (X0{\unicdcdgdad}k1\_xxreal\_0){\unicdcdcdhd}((X1{\unicdcdgdad}k2\_xxreal\_0){\unicdcdcdhd}\\
((X2{\unicdcdgdad}k2\_xxreal\_0){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k1\_xxreal\_3~X2~X1)~X0)))))))))\end{array}
\label{hyp:ehfdedpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X2)){\unicdbdjdcd}\\
(r1\_xxreal\_0~X0~X2))))\end{array}
\label{hyp:ehcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k7\_numbers){\unicdbdjdcd}(r1\_xxreal\_0~(k4\_supinf\_2~X1~X0)~(k3\_extreal1~\\
(k4\_supinf\_2~X0~X1))))\end{array}
\label{hyp:ehcdpfngfgdhggfhogdgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k7\_numbers)){\unicdbdjdcd}(k4\_supinf\_2~X0~X1=k3\_xxreal\_3~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_supinf\_1}={k2\_xxreal\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfdhfhahjgogggpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_supinf\_1}={k1\_xxreal\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhfhahjgogggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k7\_numbers)){\unicdbdjdcd}(m1\_subset\_1~(k4\_supinf\_2~X0~X1)~k7\_numbers)\end{array}
\label{hyp:egehpflgedpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k3\_extreal1~\\
X0)~k7\_numbers)\end{array}
\label{hyp:egehpflgddpffgihehchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k7\_numbers}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddpfngfgdhggfhogdgfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k7\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~\\
X2~(k3\_extreal1~(k4\_supinf\_2~X0~X1))){\unicdcdcdhd}((\preoh (X0=k1\_supinf\_1){\unicdcdcdhd}(\\
X1=k1\_supinf\_1)){\unicdcdcdhd}((\preoh (X0=k2\_supinf\_1){\unicdcdcdhd}(X1=k2\_supinf\_1)){\unicdcdcdhd}\\
(\preoh (X0{\unicdcdgdad}k1\_supinf\_1){\unicdcdcdhd}((X0{\unicdcdgdad}k2\_supinf\_1){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_supinf\_1){\unicdcdcdhd}\\
(X1{\unicdcdgdad}k2\_supinf\_1)))))))))\end{array}$$
\end{theorem}
\end{document}
