\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{t34\_chain\_1 (TMGtXDuddk9nCnJb8iSJnHXjzmEGKRnGPL7)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m2\_subset\_1~X1~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k1\_numbers~(k1\_euclid~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_chain\_1~\\
X4~X1){\unicdbdjdcd}((r1\_xxreal\_0~X0~X1){\unicdbdjdcd}((k3\_chain\_1~X1~X2~X3 \in k4\_chain\_1~X1~\\
X4~X0){\unicdbdjded}(\preoh ({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_finseq\_1~\\
X1))){\unicdbdjdcd}(\preoh (k5\_card\_1~X5=X0){\unicdcdcdhd}({\unicdcdadad} X6 .  (m2\_subset\_1~X6~k5\_numbers~\\
(k2\_finseq\_1~X1)){\unicdbdjdcd}(((X6 \in X5){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k1\_seq\_1~X3~X6)~\\
(k1\_seq\_1~X2~X6)){\unicdcdcdhd}(m2\_chain\_1~(k1\_domain\_1~k1\_numbers~k1\_numbers~\\
(k1\_seq\_1~X2~X6)~(k1\_seq\_1~X3~X6))~(k2\_chain\_1~X1~X4~X6)))){\unicdcdcdid}((\preoh X6 \in \\
X5){\unicdcdcdhd}((k1\_seq\_1~X2~X6=k1\_seq\_1~X3~X6){\unicdcdcdhd}(k1\_seq\_1~X2~X6 \in k2\_chain\_1~\\
X1~X4~X6))))))){\unicdcdcdhd}(\preoh (X0=X1){\unicdcdcdhd}({\unicdcdadad} X5 .  (m2\_subset\_1~X5~k5\_numbers~\\
(k2\_finseq\_1~X1)){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k1\_seq\_1~X2~X5)~(k1\_seq\_1~X3~\\
X5)){\unicdcdcdhd}(m2\_chain\_1~(k1\_domain\_1~k1\_numbers~k1\_numbers~(k1\_seq\_1~\\
X2~X5)~(k1\_seq\_1~X3~X5))~(k2\_chain\_1~X1~X4~X5))))))))))))\end{array}
\label{hyp:ehddddpfdgigbgjgogpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddedpfdgigbgjgogpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m2\_subset\_1~X1~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k1\_numbers~(k1\_euclid~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_chain\_1~\\
X4~X1){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((k3\_chain\_1~X1~X2~X3 \in k4\_chain\_1~\\
X1~X4~X0){\unicdcdcdhd}(({\unicdcdaddd} X5 .  (m2\_subset\_1~X5~k5\_numbers~(k2\_finseq\_1~\\
X1)){\unicdcdcdhd}((\preoh (\preoh r1\_xxreal\_0~(k1\_seq\_1~X3~X5)~(k1\_seq\_1~X2~X5)){\unicdcdcdhd}(m2\_chain\_1~\\
(k1\_domain\_1~k1\_numbers~k1\_numbers~(k1\_seq\_1~X2~X5)~(k1\_seq\_1~\\
X3~X5))~(k2\_chain\_1~X1~X4~X5))){\unicdcdcdhd}(\preoh (k1\_seq\_1~X2~X5=k1\_seq\_1~X3~X5){\unicdcdcdhd}\\
(k1\_seq\_1~X2~X5 \in k2\_chain\_1~X1~X4~X5)))){\unicdcdcdhd}(\preoh {\unicdcdadad} X5 .  (m2\_subset\_1~\\
X5~k5\_numbers~(k2\_finseq\_1~X1)){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k1\_seq\_1~X2~X5)~\\
(k1\_seq\_1~X3~X5)){\unicdcdcdhd}(m2\_chain\_1~(k1\_domain\_1~k1\_numbers~k1\_numbers~\\
(k1\_seq\_1~X2~X5)~(k1\_seq\_1~X3~X5))~(k2\_chain\_1~X1~X4~X5)))))))))))\end{array}$$
\end{theorem}
\end{document}
