\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{t18\_limfunc1 (TMRqzH383rUZ9V5YxgnBWw8D1ijrYZkNfJA)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ v1\_limfunc1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v2\_seq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_seq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(((v1\_limfunc1~X0){\unicdcdcdhd}(v2\_seq\_2~X1)){\unicdbdjdcd}(v1\_limfunc1~(k3\_valued\_1~\\
k5\_numbers~k1\_numbers~k1\_numbers~X0~X1))))\end{array}
\label{hyp:ehjdpfmgjgngggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
k1\_numbers))){\unicdbdjdcd}(((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~\\
k1\_numbers){\unicdcdcdhd}(v2\_comseq\_2~X0))){\unicdbdjdcd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~\\
X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}(v1\_comseq\_2~X0))))\end{array}
\label{hyp:dgdgedpfdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v3\_valued\_0~\\
X0){\unicdcdcdhd}(v1\_comseq\_2~X0)))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}\\
((v3\_valued\_0~X0){\unicdcdcdhd}((v1\_seq\_2~X0){\unicdcdcdhd}(v2\_seq\_2~X0)))))\end{array}
\label{hyp:dgdgbdpfdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v3\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v3\_valued\_0~X2))\end{array}
\label{hyp:dgdgbdidpfghbgmgfhfgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfmgjgngggfhogdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(((v1\_limfunc1~X0){\unicdcdcdhd}(v2\_comseq\_2~X1)){\unicdbdjdcd}(v1\_limfunc1~(k3\_valued\_1~\\
k5\_numbers~k1\_numbers~k1\_numbers~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
