\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{t31\_rpr\_1 (TMM8vKg5TXFPwXanoZsynNMrsFkiWKQQQXx)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_rpr\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k1\_rpr\_1~X0~(k7\_subset\_1~X0~X1~X2)=k9\_real\_1~\\
(k1\_rpr\_1~X0~X1)~(k1\_rpr\_1~X0~(k9\_subset\_1~X0~X1~X2)))))\end{array}
\label{hyp:ehcdddpfchahchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~X0)){\unicdbdjdcd}((r1\_tarski~X1~X2){\unicdbdjdcd}(r1\_xxreal\_0~(k1\_rpr\_1~\\
X0~X1)~(k1\_rpr\_1~X0~X2)))))\end{array}
\label{hyp:ehbdjdpfchahchpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{({{{k3\_xboole\_0}~{X0}}~{X1}})}}~{X0}}}}\label{hyp:ehbdhdpfihcgpgpgmgfgpfbd}
\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 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X2~X3)){\unicdbdjdcd}(r1\_xxreal\_0~(k6\_xcmplx\_0~X0~X3)~(\\
k6\_xcmplx\_0~X1~X2))))))\end{array}
\label{hyp:ehbdddpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k3\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(k9\_real\_1~X0~X1=k6\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k7\_subset\_1~X0~X1~X2=k4\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(m1\_subset\_1~(k9\_subset\_1~X0~X1~X2)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_finset\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k1\_rpr\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfchahchpfbd}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X1}}={{{k3\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihcgpgpgmgfgpfad}
\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 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfchahchpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(r1\_xxreal\_0~(k9\_real\_1~(k1\_rpr\_1~X0~X1)~(k1\_rpr\_1~\\
X0~X2))~(k1\_rpr\_1~X0~(k7\_subset\_1~X0~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
