\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{t7\_compl\_sp (TMKosPrt2JKZfrWsUNFHhX4XWzJMFSjpQDB)}
\maketitle
Let $ l1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\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 $ k3\_pcomps\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ v6\_compl\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_compl\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_compl\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_compl\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_compl\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_compl\_sp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_metric\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_pcomps\_1~X0)))){\unicdbdjdcd}((X2=X1){\unicdbdjdcd}(((v2\_compl\_sp~X1~\\
X0){\unicdbdjdcd}(v3\_pre\_topc~X2~(k3\_pcomps\_1~X0))){\unicdcdcdhd}(((v3\_pre\_topc~X2~(k3\_pcomps\_1~\\
X0)){\unicdbdjdcd}(v2\_compl\_sp~X1~X0)){\unicdcdcdhd}(((v3\_compl\_sp~X1~X0){\unicdbdjdcd}(v4\_pre\_topc~\\
X2~(k3\_pcomps\_1~X0))){\unicdcdcdhd}((v4\_pre\_topc~X2~(k3\_pcomps\_1~X0)){\unicdbdjdcd}(v3\_compl\_sp~\\
X1~X0))))))))\end{array}
\label{hyp:ehgdpfdgpgngahmgpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}((\\
v1\_funct\_2~X4~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))))))){\unicdbdjdcd}((r1\_funct\_2~X0~X1~\\
X2~X3~X4~X5){\unicdbdjded}(X4=X5))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0))))){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdbdjdcd}(k8\_nat\_1~X0~X1~X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_zfmisc\_1}~{X0}})}}}}}\label{hyp:ggdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0))))){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdbdjdcd}(m1\_subset\_1~(k8\_nat\_1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgidpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_metric\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_pre\_topc}~{({{k3\_pcomps\_1}~{X0}})}})}}}\label{hyp:egehpflgddpfahdgpgngahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_metric\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}((v7\_compl\_sp~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}\\
(v3\_compl\_sp~(k8\_nat\_1~(k9\_setfam\_1~(u1\_struct\_0~X0))~X1~X2)~X0))))\end{array}
\label{hyp:egidpfdgpgngahmgpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_metric\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}((v6\_compl\_sp~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}\\
(v2\_compl\_sp~(k8\_nat\_1~(k9\_setfam\_1~(u1\_struct\_0~X0))~X1~X2)~X0))))\end{array}
\label{hyp:eghdpfdgpgngahmgpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}((v5\_compl\_sp~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}\\
(v4\_pre\_topc~(k8\_nat\_1~(k9\_setfam\_1~(u1\_struct\_0~X0))~X1~X2)~X0))))\end{array}
\label{hyp:eggdpfdgpgngahmgpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}((v4\_compl\_sp~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}\\
(v3\_pre\_topc~(k8\_nat\_1~(k9\_setfam\_1~(u1\_struct\_0~X0))~X1~X2)~X0))))\end{array}
\label{hyp:egfdpfdgpgngahmgpfdhah}
\end{equation}
\begin{theorem}\label{thm:ehhdpfdgpgngahmgpfdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_metric\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~\\
(k9\_setfam\_1~(u1\_struct\_0~(k3\_pcomps\_1~X0)))){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~\\
(k3\_pcomps\_1~X0)))))))){\unicdbdjdcd}((r1\_funct\_2~k5\_numbers~(k9\_setfam\_1~\\
(u1\_struct\_0~(k3\_pcomps\_1~X0)))~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~\\
X0))~X2~X1){\unicdbdjdcd}(((v6\_compl\_sp~X1~X0){\unicdbdjdcd}(v4\_compl\_sp~X2~(k3\_pcomps\_1~\\
X0))){\unicdcdcdhd}(((v4\_compl\_sp~X2~(k3\_pcomps\_1~X0)){\unicdbdjdcd}(v6\_compl\_sp~X1~X0)){\unicdcdcdhd}\\
(((v7\_compl\_sp~X1~X0){\unicdbdjdcd}(v5\_compl\_sp~X2~(k3\_pcomps\_1~X0))){\unicdcdcdhd}((v5\_compl\_sp~\\
X2~(k3\_pcomps\_1~X0)){\unicdbdjdcd}(v7\_compl\_sp~X1~X0))))))))\end{array}$$
\end{theorem}
\end{document}
