\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{t7\_mesfunc9 (TMKUMeoxLfeCbuKDNzfoN9GyGxGJ2pP1Bja)}
\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 $ v7\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_mesfunc5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\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 $ k12\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v8\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_supinf\_1 : {\iota}$ be given.
Let $ v9\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_supinf\_1 : {\iota}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ 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}\\
((v9\_mesfunc5~X0){\unicdbdjdcd}((\preoh v8\_mesfunc5~X0){\unicdcdcdhd}(\preoh v7\_mesfunc5~X0)))\end{array}
\label{hyp:ehfdbdpfngfgdhggfhogdgfd}
\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}\\
((v8\_mesfunc5~X0){\unicdbdjdcd}((\preoh v9\_mesfunc5~X0){\unicdcdcdhd}(\preoh v7\_mesfunc5~X0)))\end{array}
\label{hyp:ehfdadpfngfgdhggfhogdgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0))))){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdbdjdcd}(k8\_nat\_1~X0~X1~X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v2\_valued\_0~\\
X0))){\unicdbdjdcd}(k12\_supinf\_2~X0~X1=k1\_funct\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{v2\_membered}~{k7\_numbers}}\label{hyp:ggdgcdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k2\_supinf\_1}}~{k7\_numbers}}\label{hyp:egehpflgcdpfdhfhahjgogggpfbd}
\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~(k2\_mesfunc5~X0)~k7\_numbers)\end{array}
\label{hyp:egehpflgcdpfngfgdhggfhogdgfd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_supinf\_1}}~{k7\_numbers}}\label{hyp:egehpflgbdpfdhfhahjgogggpfbd}
\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}\\
((v10\_mesfunc5~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k7\_numbers){\unicdbdjdcd}\\
((X1=k2\_mesfunc5~X0){\unicdbdjded}(\preoh ({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (X1=X2){\unicdcdcdhd}\\
(({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X3~k6\_numbers){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}({\unicdcdaddd} X5 .  (v7\_ordinal1~X5){\unicdcdcdhd}(\\
(r1\_xxreal\_0~X4~X5){\unicdcdcdhd}(r1\_xxreal\_0~X3~(k3\_extreal1~(k4\_supinf\_2~\\
(k8\_nat\_1~k7\_numbers~X0~X5)~X1)))))))){\unicdcdcdhd}(v7\_mesfunc5~X0)))){\unicdcdcdhd}(\\
(\preoh (X1=k1\_supinf\_1){\unicdcdcdhd}(v8\_mesfunc5~X0)){\unicdcdcdhd}(\preoh (X1=k2\_supinf\_1){\unicdcdcdhd}\\
(v9\_mesfunc5~X0)))))))\end{array}
\label{hyp:egbdcdpfngfgdhggfhogdgfd}
\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}\\
((v10\_mesfunc5~X0){\unicdbdjded}(\preoh (\preoh v7\_mesfunc5~X0){\unicdcdcdhd}((\preoh v8\_mesfunc5~X0){\unicdcdcdhd}\\
(\preoh v9\_mesfunc5~X0))))\end{array}
\label{hyp:egbdbdpfngfgdhggfhogdgfd}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v2\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v2\_valued\_0~X2))\end{array}
\label{hyp:dgdgbdhdpfghbgmgfhfgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehhdpfngfgdhggfhogdgjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
((\preoh (v7\_mesfunc5~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(\preoh (k2\_mesfunc5~\\
X0=X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdaddd} X4 .  (v7\_ordinal1~X4){\unicdcdcdhd}(\\
(r1\_xxreal\_0~X3~X4){\unicdcdcdhd}(r1\_xxreal\_0~X2~(k3\_extreal1~(k4\_supinf\_2~\\
(k12\_supinf\_2~X0~X4)~(k2\_mesfunc5~X0)))))))))))){\unicdcdcdhd}(((v8\_mesfunc5~\\
X0){\unicdbdjdcd}(k2\_mesfunc5~X0=k1\_supinf\_1)){\unicdcdcdhd}((v9\_mesfunc5~X0){\unicdbdjdcd}(k2\_mesfunc5~\\
X0=k2\_supinf\_1))))\end{array}$$
\end{theorem}
\end{document}
