\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t20\_dist\_1 (TMSgDdf2ZrZNVKoFy4N8JzTeMES6CvHmfEr)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_dist\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_dist\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_dist\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k7\_dist\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_matrprob : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_dist\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_dist\_1~X1~X0){\unicdbdjdcd}((v1\_matrprob~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k1\_numbers)))\end{array}
\label{hyp:egehpfngbdpfegjgdhehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_matrprob~X1){\unicdcdcdhd}(\\
m1\_finseq\_1~X1~k1\_numbers))){\unicdbdjdcd}(m2\_subset\_1~(k8\_dist\_1~X0~X1)~(\\
k1\_zfmisc\_1~(k3\_finseq\_2~X0))~(k6\_dist\_1~X0))\end{array}
\label{hyp:egehpflgidpfegjgdhehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrprob~X1){\unicdcdcdhd}(\\
m2\_finseq\_1~X1~k1\_numbers)){\unicdbdjdcd}(({\unicdcdaddd} X2 .  (m2\_finseq\_1~X2~X0){\unicdcdcdhd}\\
(k4\_dist\_1~X0~X2=X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k3\_finseq\_2~X0))~(k6\_dist\_1~X0)){\unicdbdjdcd}((X2=k8\_dist\_1~X0~X1){\unicdbdjded}(k3\_funct\_2~\\
(k6\_dist\_1~X0)~(k3\_finseq\_2~k1\_numbers)~(k7\_dist\_1~X0)~X2=X1)))))\end{array}
\label{hyp:egidpfegjgdhehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_matrprob~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k1\_numbers)){\unicdbdjdcd}((m1\_dist\_1~\\
X1~X0){\unicdbdjded}((k3\_finseq\_1~X1=k5\_card\_1~X0){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m2\_finseq\_1~\\
X2~X0){\unicdcdcdhd}(k4\_dist\_1~X0~X2=X1)))))\end{array}
\label{hyp:egbdadpfegjgdhehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfegjgdhehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_dist\_1~X1~X0){\unicdbdjdcd}((m2\_subset\_1~(k8\_dist\_1~X0~X1)~(k1\_zfmisc\_1~\\
(k3\_finseq\_2~X0))~(k6\_dist\_1~X0)){\unicdcdcdhd}(k3\_funct\_2~(k6\_dist\_1~X0)~\\
(k3\_finseq\_2~k1\_numbers)~(k7\_dist\_1~X0)~(k8\_dist\_1~X0~X1)=X1)))\end{array}$$
\end{theorem}
\end{document}
