\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{t62\_modelc\_3 (TMcKDwhLAAu5wT117oCFhxJNkzavvFRwbw4)}
\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 $ k25\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k43\_modelc\_2 : {\iota}$ be given.
Let $ m1\_orders\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_orders\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r7\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k26\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r8\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k14\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k25\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r4\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k22\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_modelc\_3 : {{\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 $ g1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_3~X1~X0){\unicdcdcdhd}(l1\_modelc\_3~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k25\_modelc\_2~k43\_modelc\_2)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_orders\_1~\\
X3~(k1\_orders\_1~(k1\_modelc\_3~X0))){\unicdbdjdcd}((r8\_modelc\_2~X2~(k14\_modelc\_3~\\
X0~X1)){\unicdbdjdcd}((v3\_modelc\_3~X1~X0){\unicdcdcdid}((r8\_modelc\_2~X2~(k14\_modelc\_3~X0~\\
(k25\_modelc\_3~X2~X0~X3~X1))){\unicdcdcdhd}(r4\_modelc\_3~X0~X1~(k25\_modelc\_3~X2~\\
X0~X3~X1))))))))\end{array}
\label{hyp:ehfdjdpfngpgegfgmgdgpfdd}
\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X0~(k25\_modelc\_2~\\
k43\_modelc\_2)){\unicdcdcdhd}(((v1\_modelc\_2~X1){\unicdcdcdhd}(m1\_finseq\_1~X1~k5\_numbers)){\unicdcdcdhd}\\
(m1\_orders\_1~X2~(k1\_orders\_1~(k1\_modelc\_3~X1))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k26\_modelc\_3~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k26\_modelc\_3~X0~X1~X2)~(\\
k22\_modelc\_3~X1)~(k22\_modelc\_3~X1)){\unicdcdcdhd}(m1\_subset\_1~(k26\_modelc\_3~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k22\_modelc\_3~X1)~(k22\_modelc\_3~\\
X1))))))\end{array}
\label{hyp:egehpflgcdgdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X0~\\
(k25\_modelc\_2~k43\_modelc\_2)){\unicdcdcdhd}(((v1\_modelc\_2~X1){\unicdcdcdhd}(m1\_finseq\_1~\\
X1~k5\_numbers)){\unicdcdcdhd}((m1\_orders\_1~X2~(k1\_orders\_1~(k1\_modelc\_3~X1))){\unicdcdcdhd}\\
((v1\_modelc\_3~X3~X1){\unicdcdcdhd}(l1\_modelc\_3~X3~X1))))){\unicdbdjdcd}((v1\_modelc\_3~(\\
k25\_modelc\_3~X0~X1~X2~X3)~X1){\unicdcdcdhd}(l1\_modelc\_3~(k25\_modelc\_3~X0~X1~X2~\\
X3)~X1))\end{array}
\label{hyp:egehpflgcdfdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m1\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
((v1\_modelc\_3~(k10\_modelc\_3~X0~X1)~X1){\unicdcdcdhd}(l1\_modelc\_3~(k10\_modelc\_3~\\
X0~X1)~X1))\end{array}
\label{hyp:egehpflgbdadpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k25\_modelc\_2~k43\_modelc\_2)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_orders\_1~X2~(k1\_orders\_1~(k1\_modelc\_3~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k22\_modelc\_3~X1)~(k22\_modelc\_3~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k22\_modelc\_3~\\
X1)~(k22\_modelc\_3~X1)))))){\unicdbdjdcd}((X3=k26\_modelc\_3~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  \\
(X4 \in k22\_modelc\_3~X1){\unicdbdjdcd}(k1\_funct\_1~X3~X4=k25\_modelc\_3~X0~X1~X2~(\\
k10\_modelc\_3~X4~X1)))))))\end{array}
\label{hyp:egddgdpfngpgegfgmgdgpfdd}
\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~(k25\_modelc\_2~k43\_modelc\_2)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((r7\_modelc\_3~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  \\
((X3 \in k22\_modelc\_3~X0){\unicdcdcdhd}(r8\_modelc\_2~X1~(k14\_modelc\_3~X0~(k10\_modelc\_3~\\
X3~X0)))){\unicdbdjdcd}((v3\_modelc\_3~(k10\_modelc\_3~X3~X0)~X0){\unicdcdcdid}((r4\_modelc\_3~\\
X0~(k10\_modelc\_3~X3~X0)~(k10\_modelc\_3~(k1\_funct\_1~X2~X3)~X0)){\unicdcdcdhd}(\\
r8\_modelc\_2~X1~(k14\_modelc\_3~X0~(k10\_modelc\_3~(k1\_funct\_1~X2~X3)~\\
X0)))))))))\end{array}
\label{hyp:egddcdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
((((v1\_modelc\_3~X0~X1){\unicdcdcdhd}(l1\_modelc\_3~X0~X1)){\unicdbdjdcd}(k10\_modelc\_3~X0~\\
X1=X0)){\unicdcdcdhd}((\preoh (v1\_modelc\_3~X0~X1){\unicdcdcdhd}(l1\_modelc\_3~X0~X1)){\unicdbdjdcd}(k10\_modelc\_3~\\
X0~X1=g1\_modelc\_3~X1~(k7\_modelc\_3~X1)~(k7\_modelc\_3~X1)~(k7\_modelc\_3~\\
X1))))\end{array}
\label{hyp:egbdgdpfngpgegfgmgdgpfdd}
\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:ehgdcdpfngpgegfgmgdgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k25\_modelc\_2~k43\_modelc\_2)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_orders\_1~X2~(k1\_orders\_1~(k1\_modelc\_3~X0))){\unicdbdjdcd}(r7\_modelc\_3~\\
X0~X1~(k26\_modelc\_3~X1~X0~X2))))\end{array}$$
\end{theorem}
\end{document}
