\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t36\_limfunc3 (TMPDWKdywcvGxiBHyx4jbssdHddXW1ShdW9)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_limfunc3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k56\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_limfunc3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r4\_limfunc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_limfunc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_limfunc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_limfunc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
((r4\_limfunc2~X1~X0){\unicdbdjdcd}((r4\_limfunc2~(k56\_valued\_1~k1\_numbers~\\
k1\_numbers~X1)~X0){\unicdcdcdhd}(k2\_limfunc2~(k56\_valued\_1~k1\_numbers~k1\_numbers~\\
X1)~X0=k18\_complex1~(k2\_limfunc2~X1~X0)))))\end{array}
\label{hyp:ehfdhdpfmgjgngggfhogdgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
((r1\_limfunc2~X1~X0){\unicdbdjdcd}((r1\_limfunc2~(k56\_valued\_1~k1\_numbers~\\
k1\_numbers~X1)~X0){\unicdcdcdhd}(k1\_limfunc2~(k56\_valued\_1~k1\_numbers~k1\_numbers~\\
X1)~X0=k18\_complex1~(k1\_limfunc2~X1~X0)))))\end{array}
\label{hyp:ehedidpfmgjgngggfhogdgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
(((r1\_limfunc2~X1~X0){\unicdcdcdhd}((r4\_limfunc2~X1~X0){\unicdcdcdhd}(k1\_limfunc2~X1~X0=\\
k2\_limfunc2~X1~X0))){\unicdbdjdcd}((r1\_limfunc3~X1~X0){\unicdcdcdhd}((k1\_limfunc3~X1~X0=\\
k1\_limfunc2~X1~X0){\unicdcdcdhd}(k1\_limfunc3~X1~X0=k2\_limfunc2~X1~X0)))))\end{array}
\label{hyp:ehddadpfmgjgngggfhogdgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
((r1\_limfunc3~X1~X0){\unicdbdjdcd}((r1\_limfunc2~X1~X0){\unicdcdcdhd}((r4\_limfunc2~X1~X0){\unicdcdcdhd}\\
((k1\_limfunc2~X1~X0=k2\_limfunc2~X1~X0){\unicdcdcdhd}((k1\_limfunc3~X1~X0=k1\_limfunc2~\\
X1~X0){\unicdcdcdhd}(k1\_limfunc3~X1~X0=k2\_limfunc2~X1~X0)))))))\end{array}
\label{hyp:ehcdjdpfmgjgngggfhogdgdd}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_membered}~{k1\_numbers}}\label{hyp:ggdgddpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_membered~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k56\_valued\_1~X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k56\_valued\_1~X0~X1~X2)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers))))\end{array}
\label{hyp:egehpflgfdgdpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v1\_membered}~{X0}})}}}\label{hyp:dgdgfdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfmgjgngggfhogdgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
((r1\_limfunc3~X1~X0){\unicdbdjdcd}((r1\_limfunc3~(k56\_valued\_1~k1\_numbers~\\
k1\_numbers~X1)~X0){\unicdcdcdhd}(k1\_limfunc3~(k56\_valued\_1~k1\_numbers~k1\_numbers~\\
X1)~X0=k18\_complex1~(k1\_limfunc3~X1~X0)))))\end{array}$$
\end{theorem}
\end{document}
