\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{t25\_chain\_1 (TMNkav7c7URMpbW5sXdvKyodYsQE4p5UG3n)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_finseq\_2~X1~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_2~X2~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~\\
X3~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}((X1 \in k3\_chain\_1~X0~X2~X3){\unicdbdjded}(\preoh (\preoh {\unicdcdadad} X4 .  \\
(m2\_subset\_1~X4~k5\_numbers~(k2\_finseq\_1~X0)){\unicdbdjdcd}((r1\_xxreal\_0~(\\
k1\_seq\_1~X2~X4)~(k1\_seq\_1~X1~X4)){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_seq\_1~X1~X4)~\\
(k1\_seq\_1~X3~X4)))){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~k5\_numbers~(k2\_finseq\_1~\\
X0)){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~(k1\_seq\_1~X2~X4)~(k1\_seq\_1~X3~X4)){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k1\_seq\_1~X1~X4)~(k1\_seq\_1~X3~X4)){\unicdcdcdid}(r1\_xxreal\_0~(k1\_seq\_1~X2~X4)~\\
(k1\_seq\_1~X1~X4))))))))))\end{array}
\label{hyp:ehcdddpfdgigbgjgogpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfdgigbgjgogpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_finseq\_2~X1~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_2~X2~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~\\
X3~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}((\preoh {\unicdcdadad} X4 .  (m2\_subset\_1~X4~k5\_numbers~\\
(k2\_finseq\_1~X0)){\unicdbdjdcd}(r1\_xxreal\_0~(k1\_seq\_1~X2~X4)~(k1\_seq\_1~X1~X4))){\unicdbdjdcd}\\
((X3 \in k3\_chain\_1~X0~X2~X1){\unicdbdjded}({\unicdcdaddd} X4 .  (m2\_subset\_1~X4~k5\_numbers~\\
(k2\_finseq\_1~X0)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k1\_seq\_1~X2~X4)~(k1\_seq\_1~X1~\\
X4)){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_seq\_1~X3~X4)~(k1\_seq\_1~X1~X4)){\unicdcdcdid}(r1\_xxreal\_0~\\
(k1\_seq\_1~X2~X4)~(k1\_seq\_1~X3~X4))))))))))\end{array}$$
\end{theorem}
\end{document}
