\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\_sppol\_2 (TMNLZCXSACfyvW2jo3eSKzKnaiWBqb8yHCa)}
\maketitle
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 $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_topreal4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_topreal4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_sppol\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v1\_topreal4~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}(((X1 \in X0){\unicdcdcdhd}(X2 \in X0)){\unicdbdjdcd}((X1=X2){\unicdcdcdid}(r1\_sppol\_2~\\
X1~X2~X0))))))\end{array}
\label{hyp:ehfdidpfdhahahpgmgpfcd}
\end{equation}
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}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(m1\_finseq\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k3\_topreal1~X0~X1)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~X0))))\end{array}
\label{hyp:egehpflgddpfehpgahchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}((r1\_topreal4~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v4\_topreal1~X3){\unicdcdcdhd}((X0=k3\_topreal1~\\
np\_\_2~X3){\unicdcdcdhd}((X1=k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X3~np\_\_1){\unicdcdcdhd}(X2=k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X3~\\
(k3\_finseq\_1~X3)))))))))\end{array}
\label{hyp:egbdpfehpgahchfgbgmged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((r1\_sppol\_2~X0~X1~X2){\unicdbdjded}((X0{\unicdcdgdad}X1){\unicdcdcdhd}({\unicdcdaddd} X3 .  ((v4\_topreal1~\\
X3){\unicdcdcdhd}(m2\_finseq\_1~X3~(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdcdcdhd}({\unicdcdaddd} X4 .  \\
((v4\_topreal1~X4){\unicdcdcdhd}(m2\_finseq\_1~X4~(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdcdcdhd}\\
((X0=k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X3~np\_\_1){\unicdcdcdhd}\\
((X0=k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X4~np\_\_1){\unicdcdcdhd}\\
((X1=k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X3~(k3\_finseq\_1~\\
X3)){\unicdcdcdhd}((X1=k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X4~(k3\_finseq\_1~\\
X4)){\unicdcdcdhd}((k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k3\_topreal1~\\
np\_\_2~X3)~(k3\_topreal1~np\_\_2~X4)=k2\_tarski~X0~X1){\unicdcdcdhd}(X2=k4\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k3\_topreal1~np\_\_2~X3)~(k3\_topreal1~\\
np\_\_2~X4)))))))))))))\end{array}
\label{hyp:egbdpfdhahahpgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehfdjdpfdhahahpgmgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v1\_topreal4~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}((X1 \in X0){\unicdcdcdhd}((X2 \in X0){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}(\preoh (r1\_topreal4~X3~X1~X2){\unicdcdcdhd}((r1\_topreal4~X4~X1~X2){\unicdcdcdhd}((\\
k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X3~X4=k2\_tarski~\\
X1~X2){\unicdcdcdhd}(X0=k4\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X3~X4))))))))))))\end{array}$$
\end{theorem}
\end{document}
