\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{t27\_rcomp\_3 (TMFKoJVup2NwqabvW6gmmeQihroBLZBUnFt)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_xxreal\_2 : {{\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\_numbers : {\iota}$ be given.
Let $ v3\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_limfunc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ k3\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_membered~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xxreal\_2~\\
X0){\unicdcdcdhd}((\preoh v2\_xxreal\_2~X0){\unicdcdcdhd}(v6\_xxreal\_2~X0))))){\unicdbdjdcd}(X0=k4\_xxreal\_1~\\
(k2\_xxreal\_2~X0)~(k1\_xxreal\_2~X0))\end{array}
\label{hyp:ehhdidpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}((v4\_xxreal\_2~X0){\unicdbdjded}(k1\_xxreal\_2~\\
X0{\unicdcdgdad}k1\_xxreal\_0))\end{array}
\label{hyp:ehhdddpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(k5\_seq\_4~\\
X0=k3\_seq\_4~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v3\_membered~X0){\unicdcdcdhd}(v3\_xxreal\_2~\\
X0))){\unicdbdjdcd}(k3\_seq\_4~X0=k2\_xxreal\_2~X0)\end{array}
\label{hyp:jgfgbdpfdhfgbhpfed}
\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 .  ((v3\_membered~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_xxreal\_2~\\
X0))){\unicdbdjdcd}((v1\_xxreal\_0~(k2\_xxreal\_2~X0)){\unicdcdcdhd}(v1\_xreal\_0~(k2\_xxreal\_2~\\
X0)))\end{array}
\label{hyp:ggdgcdpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_membered~X0){\unicdbdjdcd}((v1\_xxreal\_2~X0){\unicdbdjded}((v3\_xxreal\_2~\\
X0){\unicdcdcdhd}(k3\_seq\_4~X0 \in X0)))\end{array}
\label{hyp:egfdpfngfgbgdhfhchfggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(k3\_limfunc1~X0=k4\_xxreal\_1~X0~k1\_xxreal\_0)\end{array}
\label{hyp:egddpfmgjgngggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v2\_membered}~{X0}})}}}\label{hyp:dgdgedpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v3\_membered~X1))\end{array}
\label{hyp:dgdgcdbdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_membered~X0){\unicdcdcdhd}(v2\_xxreal\_2~X0)){\unicdbdjdcd}((v3\_membered~\\
X0){\unicdcdcdhd}(v4\_xxreal\_2~X0))\end{array}
\label{hyp:dgdgbdbdpfihihchfgbgmgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfchdgpgngahpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}((v3\_xxreal\_2~X0){\unicdbdjdcd}((v4\_xxreal\_2~\\
X0){\unicdcdcdid}((k5\_seq\_4~X0 \in X0){\unicdcdcdid}(X0=k3\_limfunc1~(k5\_seq\_4~X0)))))\end{array}$$
\end{theorem}
\end{document}
