\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{t48\_sprect\_2 (TMMCvKZCGoxzfB6aQb3aSDWWxNgancNAxkD)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_goboard5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_goboard5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_finseq\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\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 $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}\\
((\preoh v3\_funct\_1~X4){\unicdcdcdhd}((v1\_finseq\_6~X4~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X4){\unicdcdcdhd}((v2\_topreal1~X4){\unicdcdcdhd}((v1\_goboard5~\\
X4){\unicdcdcdhd}((v2\_goboard5~X4){\unicdcdcdhd}(m2\_finseq\_1~X4~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))))))))){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}\\
((r1\_xxreal\_0~X2~X3){\unicdcdcdhd}(r1\_xxreal\_0~X3~(k3\_finseq\_1~X4))))){\unicdbdjdcd}((\\
r1\_xxreal\_0~X2~X1){\unicdcdcdid}(((r1\_xxreal\_0~X0~np\_\_1){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_finseq\_1~\\
X4)~X3)){\unicdcdcdid}(r1\_xboole\_0~(k3\_topreal1~np\_\_2~(k3\_finseq\_6~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X4~X0~X1))~(k3\_topreal1~np\_\_2~(k3\_finseq\_6~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X4~X2~X3))))))))))\end{array}
\label{hyp:ehedhdpfdhahchfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(k3\_topreal1~np\_\_2~X0=k3\_topreal1~np\_\_2~(k4\_finseq\_5~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0))\end{array}
\label{hyp:ehcdcdpfdhahahpgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k5\_numbers){\unicdbdjdcd}(k3\_finseq\_6~X0~X1~X2~X3=k4\_finseq\_5~X0~(k3\_finseq\_6~\\
X0~X1~X3~X2)))))\end{array}
\label{hyp:ehbdidpfkgpgchegbgoged}
\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 .  (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 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((m1\_finseq\_1~X1~X0){\unicdcdcdhd}((v7\_ordinal1~X2){\unicdcdcdhd}(v7\_ordinal1~X3)))){\unicdbdjdcd}\\
(m2\_finseq\_1~(k3\_finseq\_6~X0~X1~X2~X3)~X0)\end{array}
\label{hyp:egehpflgddpfggjgogdhfgbhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))){\unicdbdjdcd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:dgdgedpfchfgmgdhfgehpfbd}
\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:ehedidpfdhahchfgdgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}\\
((\preoh v3\_funct\_1~X4){\unicdcdcdhd}((v1\_finseq\_6~X4~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X4){\unicdcdcdhd}((v2\_topreal1~X4){\unicdcdcdhd}((v1\_goboard5~\\
X4){\unicdcdcdhd}((v2\_goboard5~X4){\unicdcdcdhd}(m2\_finseq\_1~X4~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))))))))){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}\\
((r1\_xxreal\_0~X2~X3){\unicdcdcdhd}(r1\_xxreal\_0~X3~(k3\_finseq\_1~X4))))){\unicdbdjdcd}((\\
r1\_xxreal\_0~X2~X1){\unicdcdcdid}(((r1\_xxreal\_0~X0~np\_\_1){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_finseq\_1~\\
X4)~X3)){\unicdcdcdid}(r1\_xboole\_0~(k3\_topreal1~np\_\_2~(k3\_finseq\_6~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X4~X0~X1))~(k3\_topreal1~np\_\_2~(k3\_finseq\_6~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X4~X3~X2))))))))))\end{array}$$
\end{theorem}
\end{document}
