\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{t35\_limfunc3 (TMH2FQonjpygtncY2kcvD4vjBjAzQcHdAC8)}
\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 $ k8\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_limfunc3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_rfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r4\_limfunc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ 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 $ k4\_rfunct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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){\unicdcdcdhd}(k8\_relset\_1~k1\_numbers~k1\_numbers~X1~(\\
k1\_tarski~k6\_numbers)=k1\_xboole\_0)){\unicdbdjdcd}((k2\_limfunc2~X1~X0=k6\_numbers){\unicdcdcdid}\\
((r4\_limfunc2~(k6\_rfunct\_1~k1\_numbers~k1\_numbers~X1)~X0){\unicdcdcdhd}(k2\_limfunc2~\\
(k6\_rfunct\_1~k1\_numbers~k1\_numbers~X1)~X0=k2\_real\_1~(k2\_limfunc2~\\
X1~X0))))))\end{array}
\label{hyp:ehfdgdpfmgjgngggfhogdgcd}
\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}(k8\_relset\_1~k1\_numbers~k1\_numbers~X1~(\\
k1\_tarski~k6\_numbers)=k1\_xboole\_0)){\unicdbdjdcd}((k1\_limfunc2~X1~X0=k6\_numbers){\unicdcdcdid}\\
((r1\_limfunc2~(k6\_rfunct\_1~k1\_numbers~k1\_numbers~X1)~X0){\unicdcdcdhd}(k1\_limfunc2~\\
(k6\_rfunct\_1~k1\_numbers~k1\_numbers~X1)~X0=k2\_real\_1~(k1\_limfunc2~\\
X1~X0))))))\end{array}
\label{hyp:ehedhdpfmgjgngggfhogdgcd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(k8\_relset\_1~X0~X1~X2~X3=k8\_relat\_1~\\
X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v3\_membered~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}(k6\_rfunct\_1~\\
X0~X1~X2=k4\_rfunct\_1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfchggfhogdgehpfbd}
\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 .  ((v3\_membered~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k6\_rfunct\_1~X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k6\_rfunct\_1~X0~X1~X2)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k1\_numbers))))\end{array}
\label{hyp:egehpflggdpfchggfhogdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfmgjgngggfhogdgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
(((r1\_limfunc3~X1~X0){\unicdcdcdhd}(k8\_relat\_1~X1~(k1\_tarski~k6\_numbers)=\\
k1\_xboole\_0)){\unicdbdjdcd}((k1\_limfunc3~X1~X0=k6\_numbers){\unicdcdcdid}((r1\_limfunc3~\\
(k6\_rfunct\_1~k1\_numbers~k1\_numbers~X1)~X0){\unicdcdcdhd}(k1\_limfunc3~(k6\_rfunct\_1~\\
k1\_numbers~k1\_numbers~X1)~X0=k2\_real\_1~(k1\_limfunc3~X1~X0))))))\end{array}$$
\end{theorem}
\end{document}
