\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=}
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\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t34\_modelc\_3 (TMQzkFJCLwBNyB17rPLAUgsH2YEMKAeK51A)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ 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 $ r5\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_modelc\_3 : {{\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 $ k7\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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}\\
(((r5\_modelc\_3~X1~X0){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X0)){\unicdcdcdhd}\\
(u2\_modelc\_3~X1~(k10\_modelc\_3~(k1\_funct\_1~X0~(k3\_finseq\_1~X0))~\\
X1)=k7\_modelc\_3~X1))){\unicdbdjdcd}(r1\_tarski~(u2\_modelc\_3~X1~(k10\_modelc\_3~\\
(k1\_funct\_1~X0~np\_\_1)~X1))~(u1\_modelc\_3~X1~(k10\_modelc\_3~(k1\_funct\_1~\\
X0~(k3\_finseq\_1~X0))~X1)))))\end{array}
\label{hyp:ehddddpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_modelc\_2~\\
X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}(\preoh (r5\_modelc\_3~X2~X1){\unicdcdcdhd}((r1\_xxreal\_0~\\
np\_\_1~X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~(k3\_finseq\_1~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_finseq\_1~X3))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_finseq\_1~X4))){\unicdbdjdcd}(\preoh (r5\_modelc\_3~X2~X4){\unicdcdcdhd}\\
((X1=k7\_finseq\_1~X3~X4){\unicdcdcdhd}((k1\_funct\_1~X4~np\_\_1=k1\_funct\_1~X1~X0){\unicdcdcdhd}\\
((r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X4)){\unicdcdcdhd}((k3\_finseq\_1~X4=k9\_real\_1~\\
(k3\_finseq\_1~X1)~(k5\_real\_1~X0~np\_\_1)){\unicdcdcdhd}(k1\_funct\_1~X4~(k3\_finseq\_1~\\
X4)=k1\_funct\_1~X1~(k3\_finseq\_1~X1))))))))))))))\end{array}
\label{hyp:mgddedpfngpgegfgmgdgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddedpfngpgegfgmgdgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_modelc\_2~\\
X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}(((r5\_modelc\_3~X2~X1){\unicdcdcdhd}((r1\_xxreal\_0~\\
np\_\_1~X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~(k3\_finseq\_1~X1)){\unicdcdcdhd}(u2\_modelc\_3~X2~\\
(k10\_modelc\_3~(k1\_funct\_1~X1~(k3\_finseq\_1~X1))~X2)=k7\_modelc\_3~\\
X2)))){\unicdbdjdcd}(r1\_tarski~(u2\_modelc\_3~X2~(k10\_modelc\_3~(k1\_funct\_1~\\
X1~X0)~X2))~(u1\_modelc\_3~X2~(k10\_modelc\_3~(k1\_funct\_1~X1~(k3\_finseq\_1~\\
X1))~X2))))))\end{array}$$
\end{theorem}
\end{document}
