\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{t74\_rinfsup1 (TMb7Bayytej2BtQA2WmXYfaC2C5WEfY9rki)}
\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 $ k1\_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 $ v8\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_seq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_rinfsup1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_rinfsup1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_rinfsup1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_seq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_rinfsup1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v7\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}(((\\
v8\_valued\_0~X1){\unicdcdcdhd}(v2\_seq\_2~X1)){\unicdbdjdcd}((k1\_seq\_1~(k3\_rinfsup1~X1)~X0=\\
k2\_rinfsup1~X1){\unicdcdcdhd}(v3\_funct\_1~(k3\_rinfsup1~X1)))))\end{array}
\label{hyp:ehhdddpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v1\_seq\_2~X0){\unicdbdjdcd}(k1\_seq\_1~(k4\_rinfsup1~X0)~k6\_numbers=k1\_rinfsup1~\\
X0))\end{array}
\label{hyp:ehddjdpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v2\_seq\_2~X0){\unicdbdjdcd}(k1\_seq\_1~(k3\_rinfsup1~X0)~k6\_numbers=k2\_rinfsup1~\\
X0))\end{array}
\label{hyp:ehddidpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(((v7\_valued\_0~X0){\unicdbdjdcd}(v2\_seq\_2~X0)){\unicdcdcdhd}((v8\_valued\_0~X0){\unicdbdjdcd}(v1\_seq\_2~\\
X0)))\end{array}
\label{hyp:ehbdpfmgjgngggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}((v8\_valued\_0~\\
X1){\unicdbdjdcd}(k1\_seq\_1~(k4\_rinfsup1~X1)~X0=k1\_seq\_1~X1~X0)))\end{array}
\label{hyp:mghdhdpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
{{{{m2\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}~{k5\_numbers}}\label{hyp:egehpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k3\_rinfsup1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k3\_rinfsup1~X0)~\\
k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k3\_rinfsup1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgddpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
k1\_numbers))){\unicdbdjdcd}(((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_funct\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v7\_valued\_0~X0){\unicdcdcdhd}(v8\_valued\_0~X0))))\end{array}
\label{hyp:dgdgbdpfdhfgbhngpfdd}
\end{equation}
\begin{theorem}\label{thm:ehhdedpfchjgogggdhfhahbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(((v8\_valued\_0~X0){\unicdcdcdhd}(v2\_seq\_2~X0)){\unicdbdjdcd}(k1\_rinfsup1~(k3\_rinfsup1~\\
X0)=k2\_rinfsup1~X0))\end{array}$$
\end{theorem}
\end{document}
