\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{t40\_supinf\_2 (TMXUDsUcQTCe12LFFTpFyT6bQgATStBFV2m)}
\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 $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v6\_supinf\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k12\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_supinf\_2 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_card\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_supinf\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k15\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k17\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v4\_card\_3~X0){\unicdcdcdhd}((v5\_supinf\_2~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k7\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_supinf\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
((r1\_xxreal\_0~(k12\_supinf\_2~(k15\_supinf\_2~X0~X1)~X2)~(k12\_supinf\_2~\\
(k15\_supinf\_2~X0~X1)~(k2\_nat\_1~X2~np\_\_1))){\unicdcdcdhd}(r1\_xxreal\_0~k1\_supinf\_2~\\
(k12\_supinf\_2~(k15\_supinf\_2~X0~X1)~X2)))))\end{array}
\label{hyp:ehddgdpfdhfhahjgogggpfcd}
\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~\\
X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_supinf\_2}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhfhahjgogggpfcd}
\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}\\
(k17\_supinf\_2~X0=k10\_xtuple\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdhdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v4\_card\_3~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k7\_numbers)))){\unicdbdjdcd}({\unicdcdaddd} X1 .  m1\_supinf\_2~X1~X0)\end{array}
\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v4\_card\_3~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k7\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_supinf\_2~X1~X0){\unicdbdjdcd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))))\end{array}
\label{hyp:egehpfngbdpfdhfhahjgogggpfcd}
\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}\\
((v1\_funct\_1~(k18\_supinf\_2~X0)){\unicdcdcdhd}((v1\_funct\_2~(k18\_supinf\_2~\\
X0)~k5\_numbers~k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k18\_supinf\_2~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k7\_numbers)))))\end{array}
\label{hyp:egehpflgbdidpfdhfhahjgogggpfcd}
\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}\\
((\preoh v1\_xboole\_0~(k17\_supinf\_2~X0)){\unicdcdcdhd}((v4\_card\_3~(k17\_supinf\_2~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(k17\_supinf\_2~X0)~(k1\_zfmisc\_1~k7\_numbers))))\end{array}
\label{hyp:egehpflgbdhdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v4\_card\_3~X0){\unicdcdcdhd}(\\
m1\_subset\_1~X0~(k1\_zfmisc\_1~k7\_numbers)))){\unicdcdcdhd}(m1\_supinf\_2~X1~X0)){\unicdbdjdcd}\\
((v1\_funct\_1~(k15\_supinf\_2~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k15\_supinf\_2~\\
X0~X1)~k5\_numbers~k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k15\_supinf\_2~X0~X1)~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers)))))\end{array}
\label{hyp:egehpflgbdfdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((v6\_supinf\_2~X0){\unicdbdjded}(v5\_supinf\_2~(\\
k10\_xtuple\_0~X0)))\end{array}
\label{hyp:egbdgdpfdhfhahjgogggpfcd}
\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}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
((X1=k18\_supinf\_2~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_supinf\_2~X2~(k17\_supinf\_2~\\
X0)){\unicdbdjdcd}((r2\_funct\_2~k5\_numbers~k7\_numbers~X2~X0){\unicdbdjdcd}(r2\_funct\_2~k5\_numbers~\\
k7\_numbers~X1~(k15\_supinf\_2~(k17\_supinf\_2~X0)~X2))))))\end{array}
\label{hyp:egbdfdpfdhfhahjgogggpfcd}
\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:ehedadpfdhfhahjgogggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}((v6\_supinf\_2~\\
X0){\unicdbdjdcd}((r1\_xxreal\_0~(k12\_supinf\_2~(k18\_supinf\_2~X0)~X1)~(k12\_supinf\_2~\\
(k18\_supinf\_2~X0)~(k2\_nat\_1~X1~np\_\_1))){\unicdcdcdhd}(r1\_xxreal\_0~k1\_supinf\_2~\\
(k12\_supinf\_2~(k18\_supinf\_2~X0)~X1)))))\end{array}$$
\end{theorem}
\end{document}
