\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{t54\_modelc\_3 (TMaa5PgXPaCsmimt8vaLn9igFQHfVod9NSr)}
\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k23\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\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\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r6\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v7\_modelc\_2~X0){\unicdbdjdcd}(X0=k7\_modelc\_2~(k11\_modelc\_2~X0)~(k12\_modelc\_2~\\
X0)))\end{array}
\label{hyp:ehidpfngpgegfgmgdgpfcd}
\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}(m2\_finseq\_1~X0~k5\_numbers)){\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 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~(k23\_modelc\_3~\\
X2)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k23\_modelc\_3~\\
X2)))))){\unicdbdjdcd}(\preoh (k7\_modelc\_2~X0~X1 \in u1\_modelc\_3~X2~(k10\_modelc\_3~(\\
k3\_funct\_2~k5\_numbers~(k23\_modelc\_3~X2)~X3~np\_\_1)~X2)){\unicdcdcdhd}(({\unicdcdadad} X4 .  \\
(v7\_ordinal1~X4){\unicdbdjdcd}(r6\_modelc\_3~X2~(k10\_modelc\_3~(k1\_funct\_1~X3~\\
X4)~X2)~(k10\_modelc\_3~(k3\_funct\_2~k5\_numbers~(k23\_modelc\_3~X2)~\\
X3~(k1\_nat\_1~X4~np\_\_1))~X2))){\unicdcdcdhd}(({\unicdcdaddd} X4 .  (v7\_ordinal1~X4){\unicdcdcdhd}(\\
(r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}(\preoh (k7\_modelc\_2~X0~X1 \in u1\_modelc\_3~X2~(k10\_modelc\_3~\\
(k1\_funct\_1~X3~X4)~X2)){\unicdcdcdhd}((X0 \in u1\_modelc\_3~X2~(k10\_modelc\_3~(k1\_funct\_1~\\
X3~X4)~X2)){\unicdcdcdhd}(\preoh X1 \in u1\_modelc\_3~X2~(k10\_modelc\_3~(k1\_funct\_1~X3~X4)~\\
X2)))))){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~\\
X4){\unicdcdcdhd}((X1 \in u1\_modelc\_3~X2~(k10\_modelc\_3~(k1\_funct\_1~X3~X4)~X2)){\unicdcdcdhd}\\
({\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X5){\unicdbdjdcd}((r1\_xxreal\_0~\\
X4~X5){\unicdcdcdid}((k7\_modelc\_2~X0~X1 \in u1\_modelc\_3~X2~(k10\_modelc\_3~(k1\_funct\_1~\\
X3~X5)~X2)){\unicdcdcdhd}(X0 \in u1\_modelc\_3~X2~(k10\_modelc\_3~(k1\_funct\_1~X3~X5)~\\
X2)))))))))))))))\end{array}
\label{hyp:mgbdbdjdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v1\_modelc\_2~(k12\_modelc\_2~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k12\_modelc\_2~\\
X0)~k5\_numbers))\end{array}
\label{hyp:egehpflgbdcdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v1\_modelc\_2~(k11\_modelc\_2~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k11\_modelc\_2~\\
X0)~k5\_numbers))\end{array}
\label{hyp:egehpflgbdbdpfngpgegfgmgdgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehfdedpfngpgegfgmgdgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k23\_modelc\_3~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k23\_modelc\_3~\\
X1)))))){\unicdbdjdcd}(\preoh (v7\_modelc\_2~X0){\unicdcdcdhd}((X0 \in u1\_modelc\_3~X1~(k10\_modelc\_3~\\
(k3\_funct\_2~k5\_numbers~(k23\_modelc\_3~X1)~X2~np\_\_1)~X1)){\unicdcdcdhd}(({\unicdcdadad} X3 .  \\
(v7\_ordinal1~X3){\unicdbdjdcd}(r6\_modelc\_3~X1~(k10\_modelc\_3~(k1\_funct\_1~X2~\\
X3)~X1)~(k10\_modelc\_3~(k3\_funct\_2~k5\_numbers~(k23\_modelc\_3~X1)~\\
X2~(k1\_nat\_1~X3~np\_\_1))~X1))){\unicdcdcdhd}(({\unicdcdaddd} X3 .  (v7\_ordinal1~X3){\unicdcdcdhd}(\\
(r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}(\preoh (X0 \in u1\_modelc\_3~X1~(k10\_modelc\_3~(k1\_funct\_1~\\
X2~X3)~X1)){\unicdcdcdhd}((k11\_modelc\_2~X0 \in u1\_modelc\_3~X1~(k10\_modelc\_3~(k1\_funct\_1~\\
X2~X3)~X1)){\unicdcdcdhd}(\preoh k12\_modelc\_2~X0 \in u1\_modelc\_3~X1~(k10\_modelc\_3~(k1\_funct\_1~\\
X2~X3)~X1)))))){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~\\
np\_\_1~X3){\unicdcdcdhd}((k12\_modelc\_2~X0 \in u1\_modelc\_3~X1~(k10\_modelc\_3~(k1\_funct\_1~\\
X2~X3)~X1)){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~\\
X4){\unicdbdjdcd}((r1\_xxreal\_0~X3~X4){\unicdcdcdid}((X0 \in u1\_modelc\_3~X1~(k10\_modelc\_3~(\\
k1\_funct\_1~X2~X4)~X1)){\unicdcdcdhd}(k11\_modelc\_2~X0 \in u1\_modelc\_3~X1~(k10\_modelc\_3~\\
(k1\_funct\_1~X2~X4)~X1)))))))))))))))\end{array}$$
\end{theorem}
\end{document}
