\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{t59\_rcomp\_3 (TMSuAZsoKGtt4zFN2EqZdT6V66Ykpw2yVUw)}
\maketitle
Let $ v1\_xreal\_0 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_topmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_rcomp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_rcomp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ k5\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k3\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~(k4\_topmetr~\\
X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_rcomp\_3~X3~X0~X1~X2){\unicdbdjdcd}(((m1\_setfam\_1~\\
X2~(u1\_struct\_0~(k4\_topmetr~X0~X1))){\unicdcdcdhd}((v1\_tops\_2~X2~(k4\_topmetr~\\
X0~X1)){\unicdcdcdhd}((v1\_rcomp\_3~X2~(k4\_topmetr~X0~X1)){\unicdcdcdhd}(r1\_xxreal\_0~X0~X1)))){\unicdbdjdcd}\\
(r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X3))))))\end{array}
\label{hyp:ehfdbdpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((X1=k9\_finseq\_1~X0){\unicdbdjded}((k3\_finseq\_1~X1=np\_\_1){\unicdcdcdhd}(k10\_xtuple\_0~\\
X1=k1\_tarski~X0)))\end{array}
\label{hyp:ehddjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}((X0 \in k3\_xxreal\_1~X1~X2){\unicdbdjded}((\preoh r1\_xxreal\_0~X0~X1){\unicdcdcdhd}\\
(r1\_xxreal\_0~X0~X2)))))\end{array}
\label{hyp:ehcdpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}((X0 \in k1\_xxreal\_1~X1~X2){\unicdbdjded}((r1\_xxreal\_0~X1~X0){\unicdcdcdhd}\\
(r1\_xxreal\_0~X0~X2)))))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(k7\_partfun1~X0~(k12\_finseq\_1~X0~X1)~np\_\_1=X1))\end{array}
\label{hyp:ehbdgdpfggjgogdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m2\_finseq\_1~\\
X2~X1){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~(k3\_finseq\_1~\\
X2))){\unicdbdjdcd}(k7\_partfun1~X1~X2~X0=k1\_funct\_1~X2~X0)))\end{array}
\label{hyp:ehbdfdpfggjgogdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
r1\_xxreal\_0~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\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}
{{\unicdcdadad} X0 .  {{{k9\_finseq\_1}~{X0}}={{k5\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(k4\_rcomp\_1~\\
X0~X1=k3\_xxreal\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(k3\_finseq\_1~X0=k1\_card\_1~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(k1\_rcomp\_1~\\
X0~X1=k1\_xxreal\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k12\_finseq\_1~X0~X1=k5\_finseq\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}((v1\_finset\_1~(k1\_card\_1~X0)){\unicdcdcdhd}(\\
v1\_card\_1~(k1\_card\_1~X0)))\end{array}
\label{hyp:ggdggdpfdgbgchegpfbd}
\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 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_finseq\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0)))))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}((v1\_xreal\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~(\\
k4\_topmetr~X0~X1))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_rcomp\_3~X3~X0~X1~X2){\unicdbdjdcd}(\\
m2\_finseq\_1~X3~(k9\_setfam\_1~k1\_numbers)))\end{array}
\label{hyp:egehpfngbdpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))\end{array}
\label{hyp:egehpfngbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~\\
(k1\_rcomp\_1~X0~X1)~(k1\_zfmisc\_1~k1\_numbers))\end{array}
\label{hyp:egehpflgbdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_card\_1}~{({{k1\_card\_1}~{X0}})}}}\label{hyp:egehpflgbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~(k4\_topmetr~\\
X0~X1))))){\unicdbdjdcd}(((m1\_setfam\_1~X2~(u1\_struct\_0~(k4\_topmetr~X0~X1))){\unicdcdcdhd}\\
((v1\_tops\_2~X2~(k4\_topmetr~X0~X1)){\unicdcdcdhd}((v1\_rcomp\_3~X2~(k4\_topmetr~\\
X0~X1)){\unicdcdcdhd}(r1\_xxreal\_0~X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~(k9\_setfam\_1~\\
k1\_numbers)){\unicdbdjdcd}((m1\_rcomp\_3~X3~X0~X1~X2){\unicdbdjded}((r1\_tarski~(k2\_relset\_1~\\
(k9\_setfam\_1~k1\_numbers)~X3)~X2){\unicdcdcdhd}((k5\_setfam\_1~k1\_numbers~(k2\_relset\_1~\\
(k9\_setfam\_1~k1\_numbers)~X3)=k1\_rcomp\_1~X0~X1){\unicdcdcdhd}(({\unicdcdadad} X4 .  \\
(v7\_ordinal1~X4){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X4){\unicdbdjdcd}((\preoh (r1\_xxreal\_0~X4~\\
(k3\_finseq\_1~X3)){\unicdcdcdhd}(v1\_xboole\_0~(k7\_partfun1~(k9\_setfam\_1~k1\_numbers)~\\
X3~X4))){\unicdcdcdhd}(((r1\_xxreal\_0~(k1\_nat\_1~X4~np\_\_1)~(k3\_finseq\_1~X3)){\unicdbdjdcd}\\
((r1\_xxreal\_0~(k5\_seq\_4~(k7\_partfun1~(k9\_setfam\_1~k1\_numbers)~\\
X3~X4))~(k5\_seq\_4~(k7\_partfun1~(k9\_setfam\_1~k1\_numbers)~X3~(k1\_nat\_1~\\
X4~np\_\_1)))){\unicdcdcdhd}((r1\_xxreal\_0~(k4\_seq\_4~(k7\_partfun1~(k9\_setfam\_1~\\
k1\_numbers)~X3~X4))~(k4\_seq\_4~(k7\_partfun1~(k9\_setfam\_1~k1\_numbers)~\\
X3~(k1\_nat\_1~X4~np\_\_1)))){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k4\_seq\_4~(k7\_partfun1~\\
(k9\_setfam\_1~k1\_numbers)~X3~X4))~(k5\_seq\_4~(k7\_partfun1~(k9\_setfam\_1~\\
k1\_numbers)~X3~(k1\_nat\_1~X4~np\_\_1))))))){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_nat\_1~\\
X4~np\_\_2)~(k3\_finseq\_1~X3)){\unicdbdjdcd}(r1\_xxreal\_0~(k4\_seq\_4~(k7\_partfun1~\\
(k9\_setfam\_1~k1\_numbers)~X3~X4))~(k5\_seq\_4~(k7\_partfun1~(k9\_setfam\_1~\\
k1\_numbers)~X3~(k1\_nat\_1~X4~np\_\_2))))))))){\unicdcdcdhd}(((k1\_rcomp\_1~X0~X1 \in \\
X2){\unicdbdjdcd}(X3=k12\_finseq\_1~(k1\_zfmisc\_1~k1\_numbers)~(k1\_rcomp\_1~X0~\\
X1))){\unicdcdcdhd}((\preoh k1\_rcomp\_1~X0~X1 \in X2){\unicdbdjdcd}(({\unicdcdaddd} X4 .  (v1\_xreal\_0~X4){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~X4~X0){\unicdcdcdhd}((r1\_xxreal\_0~X4~X1){\unicdcdcdhd}(k1\_funct\_1~X3~np\_\_1=\\
k3\_rcomp\_1~X0~X4)))){\unicdcdcdhd}(({\unicdcdaddd} X4 .  (v1\_xreal\_0~X4){\unicdcdcdhd}((r1\_xxreal\_0~\\
X0~X4){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X1~X4){\unicdcdcdhd}(k1\_funct\_1~X3~(k3\_finseq\_1~X3)=\\
k4\_rcomp\_1~X4~X1)))){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~\\
X4~np\_\_1){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X3)~X4){\unicdcdcdhd}({\unicdcdadad} X5 .  (v1\_xreal\_0~\\
X5){\unicdbdjdcd}({\unicdcdadad} X6 .  (v1\_xreal\_0~X6){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~X0~X5){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
X6~X5){\unicdcdcdhd}((r1\_xxreal\_0~X6~X1){\unicdcdcdhd}(k1\_funct\_1~X3~X4=k2\_rcomp\_1~X5~X6)))))))))))))))))))))\end{array}
\label{hyp:egcdpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{({{v3\_ordinal1}~{X0}})}{\unicdcdcdhd}{({{v1\_finset\_1}~{X0}})}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdggdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finset\_1~X0)))\end{array}
\label{hyp:dgdgcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgbdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdjdpfchdgpgngahpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~(k4\_topmetr~\\
X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_rcomp\_3~X3~X0~X1~X2){\unicdbdjdcd}(((m1\_setfam\_1~\\
X2~(u1\_struct\_0~(k4\_topmetr~X0~X1))){\unicdcdcdhd}((v1\_tops\_2~X2~(k4\_topmetr~\\
X0~X1)){\unicdcdcdhd}((v1\_rcomp\_3~X2~(k4\_topmetr~X0~X1)){\unicdcdcdhd}(r1\_xxreal\_0~X0~X1)))){\unicdbdjdcd}\\
(X1 \in k7\_partfun1~(k9\_setfam\_1~k1\_numbers)~X3~(k3\_finseq\_1~X3))))))\end{array}$$
\end{theorem}
\end{document}
