\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{t2\_seqm\_3 (TMYv3Rs3uRuisL3VKKCrtck14tnkx6Ua75T)}
\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 $ v5\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_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~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v5\_valued\_0~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~\\
X2~X1){\unicdcdcdhd}(r1\_xxreal\_0~(k8\_nat\_1~k1\_numbers~X0~X2)~(k8\_nat\_1~k1\_numbers~\\
X0~X1))))))\end{array}
\label{hyp:ehbdpfdhfgbhngpfdd}
\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}\\
((({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}(\preoh r1\_xxreal\_0~\\
(k8\_nat\_1~k1\_numbers~X0~(k2\_nat\_1~X1~np\_\_1))~(k8\_nat\_1~k1\_numbers~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}(\preoh r1\_xxreal\_0~\\
(k8\_nat\_1~k1\_numbers~X0~(k2\_nat\_1~(k2\_nat\_1~X1~np\_\_1)~X2))~(k8\_nat\_1~\\
k1\_numbers~X0~X1))))){\unicdcdcdhd}((({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(\preoh r1\_xxreal\_0~(k8\_nat\_1~k1\_numbers~X0~(k2\_nat\_1~(k2\_nat\_1~X1~np\_\_1)~\\
X2))~(k8\_nat\_1~k1\_numbers~X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X2~X1){\unicdcdcdhd}(r1\_xxreal\_0~(k8\_nat\_1~k1\_numbers~\\
X0~X2)~(k8\_nat\_1~k1\_numbers~X0~X1)))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X2~X1){\unicdcdcdhd}(r1\_xxreal\_0~(k8\_nat\_1~k1\_numbers~\\
X0~X2)~(k8\_nat\_1~k1\_numbers~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}(\preoh r1\_xxreal\_0~(k8\_nat\_1~k1\_numbers~\\
X0~(k2\_nat\_1~X1~np\_\_1))~(k8\_nat\_1~k1\_numbers~X0~X1))))))\end{array}
\label{hyp:mgcdpfdhfgbhngpfdd}
\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}\\
((v5\_valued\_0~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(\preoh r1\_xxreal\_0~(k8\_nat\_1~k1\_numbers~X0~(k2\_nat\_1~X1~np\_\_1))~(k8\_nat\_1~\\
k1\_numbers~X0~X1))))\end{array}
\label{hyp:mgbdadpfdhfgbhngpfdd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfdhfgbhngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v5\_valued\_0~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}(\preoh r1\_xxreal\_0~\\
(k8\_nat\_1~k1\_numbers~X0~(k2\_nat\_1~(k2\_nat\_1~X1~np\_\_1)~X2))~(k8\_nat\_1~\\
k1\_numbers~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
