\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{t11\_modelc\_3 (TMEnKEwzgPToZDrxw2KugWNt1wrvALbGG14)}
\maketitle
Let $ v1\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_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 $ k13\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k17\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(k13\_modelc\_2~X1))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(k13\_modelc\_2~X1))){\unicdbdjdcd}\\
(((k10\_xtuple\_0~X0=k1\_modelc\_3~X1){\unicdcdcdhd}((v2\_funct\_1~X0){\unicdcdcdhd}(X4=k2\_xboole\_0~\\
X3~(k1\_tarski~X2)))){\unicdbdjdcd}((X2 \in X3){\unicdcdcdid}(k17\_modelc\_3~X1~X4~X0=k7\_real\_1~\\
(k17\_modelc\_3~X1~X3~X0)~(k3\_finseq\_1~X2))))))))\end{array}
\label{hyp:ehhdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
k1\_modelc\_3~X0=k13\_modelc\_2~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k13\_modelc\_2~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k18\_modelc\_3~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdidpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~\\
X0~k5\_numbers)){\unicdcdcdhd}((m1\_subset\_1~X1~(k1\_zfmisc\_1~(k13\_modelc\_2~\\
X0))){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~X2))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k17\_modelc\_3~X0~X1~X2)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdhdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k13\_modelc\_2~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}((X2=k18\_modelc\_3~X0~\\
X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_finseq\_1~\\
X3))){\unicdcdcdhd}((k10\_xtuple\_0~X3=k1\_modelc\_3~X0){\unicdcdcdhd}((v2\_funct\_1~X3){\unicdcdcdhd}(\\
X2=k17\_modelc\_3~X0~X1~X3)))))))\end{array}
\label{hyp:egcdgdpfngpgegfgmgdgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfngpgegfgmgdgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k13\_modelc\_2~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(k13\_modelc\_2~X0))){\unicdbdjdcd}\\
((X3=k2\_xboole\_0~X2~(k1\_tarski~X1)){\unicdbdjdcd}((X1 \in X2){\unicdcdcdid}(k18\_modelc\_3~\\
X0~X3=k7\_real\_1~(k18\_modelc\_3~X0~X2)~(k3\_finseq\_1~X1)))))))\end{array}$$
\end{theorem}
\end{document}
