\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{t32\_chain\_1 (TMM4e9TJdBmhdqeicusmL17rS2ti64NzaLc)}
\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 $ m1\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_card\_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.
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 .  (m1\_chain\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~X2~X0){\unicdbdjdcd}(k4\_chain\_1~X0~X1~X2=ReplSep2~\\
(toset~({\uniddcgcg} X3 : \iota .  m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~X0)))~\\
({\uniddcgcg} X3 : \iota .  toset~({\uniddcgcg} X4 : \iota .  m2\_finseq\_2~X4~k1\_numbers~(k1\_euclid~\\
X0)))~({\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  \preoh ({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(\\
k1\_zfmisc\_1~(k2\_finseq\_1~X0))){\unicdbdjdcd}(\preoh (k5\_card\_1~X5=X2){\unicdcdcdhd}({\unicdcdadad} X6 .  \\
(m2\_subset\_1~X6~k5\_numbers~(k2\_finseq\_1~X0)){\unicdbdjdcd}(((X6 \in X5){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k1\_seq\_1~X4~X6)~(k1\_seq\_1~X3~X6)){\unicdcdcdhd}(m2\_chain\_1~(k1\_domain\_1~k1\_numbers~\\
k1\_numbers~(k1\_seq\_1~X3~X6)~(k1\_seq\_1~X4~X6))~(k2\_chain\_1~X0~X1~X6)))){\unicdcdcdid}\\
((\preoh X6 \in X5){\unicdcdcdhd}((k1\_seq\_1~X3~X6=k1\_seq\_1~X4~X6){\unicdcdcdhd}(k1\_seq\_1~X3~X6 \in k2\_chain\_1~\\
X0~X1~X6))))))){\unicdcdcdhd}(\preoh (X2=X0){\unicdcdcdhd}({\unicdcdadad} X5 .  (m2\_subset\_1~X5~k5\_numbers~\\
(k2\_finseq\_1~X0)){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k1\_seq\_1~X3~X5)~(k1\_seq\_1~X4~\\
X5)){\unicdcdcdhd}(m2\_chain\_1~(k1\_domain\_1~k1\_numbers~k1\_numbers~(k1\_seq\_1~\\
X3~X5)~(k1\_seq\_1~X4~X5))~(k2\_chain\_1~X0~X1~X5))))))~({\uniddcgcg} X3 : \iota .  \\
{\uniddcgcg} X4 : \iota .  k3\_chain\_1~X0~X3~X4)))))\end{array}
\label{hyp:eghdpfdgigbgjgogpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfdgigbgjgogpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m2\_subset\_1~X1~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_chain\_1~X2~X1){\unicdbdjdcd}((r1\_xxreal\_0~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_euclid~X1))){\unicdbdjdcd}((X3 \in k4\_chain\_1~\\
X1~X2~X0){\unicdbdjded}({\unicdcdaddd} X4 .  (m2\_finseq\_2~X4~k1\_numbers~(k1\_euclid~X1)){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  (m2\_finseq\_2~X5~k1\_numbers~(k1\_euclid~X1)){\unicdcdcdhd}((X3=\\
k3\_chain\_1~X1~X4~X5){\unicdcdcdhd}(\preoh ({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_zfmisc\_1~\\
(k2\_finseq\_1~X1))){\unicdbdjdcd}(\preoh (k5\_card\_1~X6=X0){\unicdcdcdhd}({\unicdcdadad} X7 .  (m2\_subset\_1~\\
X7~k5\_numbers~(k2\_finseq\_1~X1)){\unicdbdjdcd}(((X7 \in X6){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k1\_seq\_1~\\
X5~X7)~(k1\_seq\_1~X4~X7)){\unicdcdcdhd}(m2\_chain\_1~(k1\_domain\_1~k1\_numbers~k1\_numbers~\\
(k1\_seq\_1~X4~X7)~(k1\_seq\_1~X5~X7))~(k2\_chain\_1~X1~X2~X7)))){\unicdcdcdid}((\preoh X7 \in \\
X6){\unicdcdcdhd}((k1\_seq\_1~X4~X7=k1\_seq\_1~X5~X7){\unicdcdcdhd}(k1\_seq\_1~X4~X7 \in k2\_chain\_1~\\
X1~X2~X7))))))){\unicdcdcdhd}(\preoh (X0=X1){\unicdcdcdhd}({\unicdcdadad} X6 .  (m2\_subset\_1~X6~k5\_numbers~\\
(k2\_finseq\_1~X1)){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k1\_seq\_1~X4~X6)~(k1\_seq\_1~X5~\\
X6)){\unicdcdcdhd}(m2\_chain\_1~(k1\_domain\_1~k1\_numbers~k1\_numbers~(k1\_seq\_1~\\
X4~X6)~(k1\_seq\_1~X5~X6))~(k2\_chain\_1~X1~X2~X6))))))))))))))\end{array}$$
\end{theorem}
\end{document}
