\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=}
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\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t41\_rinfsup2 (TMaJPE7tftKNLSTMG7jhw7Q8gvGTZPWa7Lg)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k7\_numbers : {\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 $ v10\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_mesfunc5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_rinfsup2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_rinfsup2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Let $ k2\_supinf\_1 : {\iota}$ be given.
Let $ k1\_supinf\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
((v10\_mesfunc5~X0){\unicdbdjded}(k6\_rinfsup2~X0=k5\_rinfsup2~X0))\end{array}
\label{hyp:ehedadpfchjgogggdhfhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}(\preoh (\preoh X0 \in k1\_numbers){\unicdcdcdhd}((X0{\unicdcdgdad}k1\_xxreal\_0){\unicdcdcdhd}\\
(X0{\unicdcdgdad}k2\_xxreal\_0)))\end{array}
\label{hyp:ehbdedpfihihchfgbgmgpfad}
\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 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
(((k6\_rinfsup2~X0=k5\_rinfsup2~X0){\unicdcdcdhd}(k6\_rinfsup2~X0 \in k1\_numbers)){\unicdbdjdcd}\\
((v10\_mesfunc5~X0){\unicdcdcdhd}((k2\_mesfunc5~X0=k6\_rinfsup2~X0){\unicdcdcdhd}(k2\_mesfunc5~\\
X0=k5\_rinfsup2~X0))))\end{array}
\label{hyp:mgfdfdpfchjgogggdhfhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
(((k6\_rinfsup2~X0=k5\_rinfsup2~X0){\unicdcdcdhd}(k6\_rinfsup2~X0=k2\_supinf\_1)){\unicdbdjdcd}\\
((v10\_mesfunc5~X0){\unicdcdcdhd}((k2\_mesfunc5~X0=k6\_rinfsup2~X0){\unicdcdcdhd}(k2\_mesfunc5~\\
X0=k5\_rinfsup2~X0))))\end{array}
\label{hyp:mgfdedpfchjgogggdhfhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
(((k6\_rinfsup2~X0=k5\_rinfsup2~X0){\unicdcdcdhd}(k6\_rinfsup2~X0=k1\_supinf\_1)){\unicdbdjdcd}\\
((v10\_mesfunc5~X0){\unicdcdcdhd}((k2\_mesfunc5~X0=k6\_rinfsup2~X0){\unicdcdcdhd}(k2\_mesfunc5~\\
X0=k5\_rinfsup2~X0))))\end{array}
\label{hyp:mgfdddpfchjgogggdhfhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k6\_rinfsup2~X0)~k7\_numbers)\end{array}
\label{hyp:egehpflggdpfchjgogggdhfhahcd}
\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:ehedbdpfchjgogggdhfhahcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
((v10\_mesfunc5~X0){\unicdbdjdcd}((k2\_mesfunc5~X0=k6\_rinfsup2~X0){\unicdcdcdhd}(k2\_mesfunc5~\\
X0=k5\_rinfsup2~X0)))\end{array}$$
\end{theorem}
\end{document}
