\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{t29\_rcomp\_3 (TMNsnv5r6u9pnF3Et1Kfa4JFHJwNMwB8S6G)}
\maketitle
Let $ v6\_xxreal\_2 : {{\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 $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_limfunc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_prob\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_limfunc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_limfunc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
(\preoh (\preoh v4\_xxreal\_2~X0){\unicdcdcdhd}((\preoh v3\_xxreal\_2~X0){\unicdcdcdhd}(X0{\unicdcdgdad}k1\_numbers)))\end{array}
\label{hyp:ehcdidpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}((v3\_xxreal\_2~X0){\unicdbdjdcd}((v4\_xxreal\_2~\\
X0){\unicdcdcdid}((k5\_seq\_4~X0 \in X0){\unicdcdcdid}(X0=k3\_limfunc1~(k5\_seq\_4~X0)))))\end{array}
\label{hyp:ehcdhdpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
(((v3\_xxreal\_2~X0){\unicdcdcdhd}(k5\_seq\_4~X0 \in X0)){\unicdbdjdcd}((v4\_xxreal\_2~X0){\unicdcdcdid}(X0=\\
k2\_limfunc1~(k5\_seq\_4~X0))))\end{array}
\label{hyp:ehcdfdpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}((v4\_xxreal\_2~X0){\unicdbdjdcd}((v3\_xxreal\_2~\\
X0){\unicdcdcdid}((k4\_seq\_4~X0 \in X0){\unicdcdcdid}(X0=k10\_prob\_1~(k4\_seq\_4~X0)))))\end{array}
\label{hyp:ehcdddpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
(((v4\_xxreal\_2~X0){\unicdcdcdhd}(k4\_seq\_4~X0 \in X0)){\unicdbdjdcd}((v3\_xxreal\_2~X0){\unicdcdcdid}(X0=\\
k1\_limfunc1~(k4\_seq\_4~X0))))\end{array}
\label{hyp:ehcdbdpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v5\_xxreal\_2~X0){\unicdcdcdhd}((v6\_xxreal\_2~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))))){\unicdbdjdcd}(\preoh (\preoh k5\_seq\_4~\\
X0 \in X0){\unicdcdcdhd}((\preoh k4\_seq\_4~X0 \in X0){\unicdcdcdhd}(X0{\unicdcdgdad}k2\_rcomp\_1~(k5\_seq\_4~X0)~(k4\_seq\_4~\\
X0))))\end{array}
\label{hyp:ehbdjdpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{{{k1\_xxreal\_1}~{X0}}~{X0}}={{k1\_tarski}~{X0}}})}}}\label{hyp:ehbdhdpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_xxreal\_2~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}((k5\_seq\_4~X0 \in X0){\unicdbdjdcd}((k4\_seq\_4~\\
X0 \in X0){\unicdcdcdid}(X0=k3\_rcomp\_1~(k5\_seq\_4~X0)~(k4\_seq\_4~X0))))\end{array}
\label{hyp:ehbdhdpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_xxreal\_2~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}((k4\_seq\_4~X0 \in X0){\unicdbdjdcd}((k5\_seq\_4~\\
X0 \in X0){\unicdcdcdid}(X0=k4\_rcomp\_1~(k5\_seq\_4~X0)~(k4\_seq\_4~X0))))\end{array}
\label{hyp:ehbdfdpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_xxreal\_2~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}(((k5\_seq\_4~X0 \in X0){\unicdcdcdhd}(k4\_seq\_4~\\
X0 \in X0)){\unicdbdjdcd}(X0=k1\_rcomp\_1~(k5\_seq\_4~X0)~(k4\_seq\_4~X0)))\end{array}
\label{hyp:ehbdddpfchdgpgngahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  \preoh (\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_zfmisc\_1~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
X0{\unicdcdgdad}k1\_tarski~X1))\end{array}
\label{hyp:ehbdddbdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}((v5\_xxreal\_2~\\
X0){\unicdbdjdcd}((v1\_xboole\_0~X0){\unicdcdcdid}((\preoh ({\unicdcdaddd} X1 .  (v1\_xreal\_0~X1){\unicdcdcdhd}({\unicdcdaddd} X2 .  \\
(v1\_xreal\_0~X2){\unicdcdcdhd}((X1 \in X0){\unicdcdcdhd}((X2 \in X0){\unicdcdcdhd}(X2{\unicdcdgdad}X1))))){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k4\_seq\_4~X0)~(k5\_seq\_4~X0))){\unicdcdcdhd}(\preoh (\preoh r1\_xxreal\_0~(k4\_seq\_4~X0)~(\\
k5\_seq\_4~X0)){\unicdcdcdhd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~\\
X2){\unicdbdjdcd}(\preoh (X1 \in X0){\unicdcdcdhd}((X2 \in X0){\unicdcdcdhd}(X2{\unicdcdgdad}X1)))))))))\end{array}
\label{hyp:ehbdcdpfdhfgbhpfed}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(k5\_seq\_4~\\
X0=k3\_seq\_4~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(k4\_seq\_4~\\
X0=k2\_seq\_4~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfgbhpfed}
\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}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k3\_seq\_4}~{X0}})}})}}}\label{hyp:egehpflgddpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k2\_seq\_4}~{X0}})}})}}}\label{hyp:egehpflgcdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_zfmisc\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X1 \in X0){\unicdcdcdhd}\\
(X2 \in X0)){\unicdbdjdcd}(X1=X2))\end{array}
\label{hyp:egbdadpfkhggngjgdhdgpfbd}
\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~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(v3\_membered~\\
X0)\end{array}
\label{hyp:dgdgidpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_membered~X0){\unicdcdcdhd}((v3\_xxreal\_2~X0){\unicdcdcdhd}(v4\_xxreal\_2~\\
X0))){\unicdbdjdcd}((v2\_membered~X0){\unicdcdcdhd}(v5\_xxreal\_2~X0))\end{array}
\label{hyp:dgdgfdpfihihchfgbgmgpfcd}
\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 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v2\_membered}~{X0}})}}}\label{hyp:dgdgedpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfchdgpgngahpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
(\preoh (\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((X0{\unicdcdgdad}k1\_numbers){\unicdcdcdhd}(({\unicdcdadad} X1 .  (v1\_xreal\_0~\\
X1){\unicdbdjdcd}(X0{\unicdcdgdad}k1\_limfunc1~X1)){\unicdcdcdhd}(({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(X0{\unicdcdgdad}\\
k10\_prob\_1~X1)){\unicdcdcdhd}(({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(X0{\unicdcdgdad}k2\_limfunc1~\\
X1)){\unicdcdcdhd}(({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(X0{\unicdcdgdad}k3\_limfunc1~X1)){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
(v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~\\
X1~X2){\unicdcdcdhd}(X0=k1\_rcomp\_1~X1~X2)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X2~X1){\unicdcdcdhd}(X0=k3\_rcomp\_1~\\
X1~X2)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~\\
X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X2~X1){\unicdcdcdhd}(X0=k4\_rcomp\_1~X1~X2)))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~\\
X2~X1){\unicdcdcdhd}(X0=k2\_rcomp\_1~X1~X2)))))))))))))\end{array}$$
\end{theorem}
\end{document}
