\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{t4\_limfunc4 (TMRxWsfQp8s6NVKX1dxQV1FJjX1T2NjBCcf)}
\maketitle
Let $ v1\_funct\_1 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v4\_limfunc1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_limfunc1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k8\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_limfunc1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_limfunc1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X2)))){\unicdbdjdcd}((r1\_tarski~(k2\_relset\_1~X0~X3)~(k1\_relset\_1~\\
X0~(k1\_partfun1~X0~X1~X1~X2~X4~X5))){\unicdbdjdcd}(r2\_funct\_2~k5\_numbers~X2~(k8\_funct\_2~\\
k5\_numbers~X2~X1~(k8\_funct\_2~k5\_numbers~X1~X0~X3~X4)~X5)~(k8\_funct\_2~\\
k5\_numbers~X2~X0~X3~(k1\_partfun1~X0~X1~X1~X2~X4~X5))))))))\end{array}
\label{hyp:ehddbdpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~\\
X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~X3))))){\unicdbdjdcd}(k1\_partfun1~X0~X1~X2~X3~X4~X5=k3\_relat\_1~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~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}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}((r1\_tarski~\\
(k2\_relset\_1~k1\_numbers~X2)~(k1\_relset\_1~k1\_numbers~(k1\_partfun1~\\
k1\_numbers~k1\_numbers~k1\_numbers~k1\_numbers~X1~X0))){\unicdbdjdcd}((r1\_tarski~\\
(k2\_relset\_1~k1\_numbers~X2)~(k1\_relset\_1~k1\_numbers~X1)){\unicdcdcdhd}(r1\_tarski~\\
(k2\_relset\_1~k1\_numbers~(k8\_funct\_2~k5\_numbers~k1\_numbers~k1\_numbers~\\
X2~X1))~(k1\_relset\_1~k1\_numbers~X0))))))\end{array}
\label{hyp:mgcdpfmgjgngggfhogdged}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X2){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X2){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X2))))){\unicdcdcdhd}((v1\_relat\_1~X4){\unicdcdcdhd}((v5\_relat\_1~\\
X4~X1){\unicdcdcdhd}(v1\_funct\_1~X4))))){\unicdbdjdcd}((v1\_funct\_1~(k8\_funct\_2~X0~X1~X2~X3~\\
X4)){\unicdcdcdhd}((v1\_funct\_2~(k8\_funct\_2~X0~X1~X2~X3~X4)~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
(k8\_funct\_2~X0~X1~X2~X3~X4)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))\end{array}
\label{hyp:egehpflgidpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k3\_relat\_1}~{X0}}~{X1}})}}}}\label{hyp:egehpflgddpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~X3))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_partfun1~X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_partfun1~X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X3))))\end{array}
\label{hyp:egehpflgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}((v5\_limfunc1~X0){\unicdbdjded}(({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~X2~X1){\unicdcdcdhd}(X2 \in k1\_relset\_1~k1\_numbers~X0)))){\unicdcdcdhd}({\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~X1){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~k1\_numbers~X1)~(k1\_relset\_1~\\
k1\_numbers~X0))){\unicdbdjdcd}(v2\_limfunc1~(k8\_funct\_2~k5\_numbers~k1\_numbers~\\
k1\_numbers~X1~X0))))))\end{array}
\label{hyp:egidpfmgjgngggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}((v4\_limfunc1~X0){\unicdbdjded}(({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~X2~X1){\unicdcdcdhd}(X2 \in k1\_relset\_1~k1\_numbers~X0)))){\unicdcdcdhd}({\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~X1){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~k1\_numbers~X1)~(k1\_relset\_1~\\
k1\_numbers~X0))){\unicdbdjdcd}(v1\_limfunc1~(k8\_funct\_2~k5\_numbers~k1\_numbers~\\
k1\_numbers~X1~X0))))))\end{array}
\label{hyp:eghdpfmgjgngggfhogdgbd}
\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}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\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}
\begin{theorem}\label{thm:ehedpfmgjgngggfhogdged}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((v4\_limfunc1~\\
X0){\unicdcdcdhd}((v5\_limfunc1~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X3~X2){\unicdcdcdhd}\\
(X3 \in k1\_relset\_1~k1\_numbers~(k1\_partfun1~k1\_numbers~k1\_numbers~\\
k1\_numbers~k1\_numbers~X0~X1))))))){\unicdbdjdcd}(v5\_limfunc1~(k1\_partfun1~\\
k1\_numbers~k1\_numbers~k1\_numbers~k1\_numbers~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
