\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{t24\_midsp\_3 (TMHZARGMVPg2X1kv5s7c64qDJKa6z6iyA4s)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v4\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k10\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k10\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_midsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_midsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k11\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_midsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0 \in X1){\unicdcdcdhd}((m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~X2)){\unicdcdcdhd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:ehfdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_midsp\_2~X1~X0){\unicdcdcdhd}(l1\_midsp\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~(u1\_midsp\_2~X0~X1))){\unicdbdjdcd}((k9\_midsp\_2~X0~X1~X2~X2=k11\_midsp\_2~\\
X0~X1){\unicdcdcdhd}(((k9\_midsp\_2~X0~X1~X2~X3=k11\_midsp\_2~X0~X1){\unicdbdjdcd}(X2=X3)){\unicdcdcdhd}(\\
(k9\_midsp\_2~X0~X1~X2~X3=k4\_algstr\_0~(u1\_midsp\_2~X0~X1)~(k9\_midsp\_2~\\
X0~X1~X3~X2)){\unicdcdcdhd}(((k9\_midsp\_2~X0~X1~X2~X3=k9\_midsp\_2~X0~X1~X4~X5){\unicdbdjdcd}(k9\_midsp\_2~\\
X0~X1~X3~X2=k9\_midsp\_2~X0~X1~X5~X4)){\unicdcdcdhd}(({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~(\\
u1\_midsp\_2~X0~X1))){\unicdbdjdcd}({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(k9\_midsp\_2~X0~X1~X9~X7=X8)))){\unicdcdcdhd}(((k9\_midsp\_2~X0~X1~X3~X2=k9\_midsp\_2~\\
X0~X1~X4~X2){\unicdbdjdcd}(X3=X4)){\unicdcdcdhd}(((k3\_midsp\_1~X0~X2~X3=X4){\unicdbdjdcd}(k9\_midsp\_2~X0~\\
X1~X2~X4=k9\_midsp\_2~X0~X1~X4~X3)){\unicdcdcdhd}(((k9\_midsp\_2~X0~X1~X2~X4=k9\_midsp\_2~\\
X0~X1~X4~X3){\unicdbdjdcd}(k3\_midsp\_1~X0~X2~X3=X4)){\unicdcdcdhd}(((k3\_midsp\_1~X0~X2~X3=k3\_midsp\_1~\\
X0~X4~X5){\unicdbdjdcd}(k9\_midsp\_2~X0~X1~X2~X5=k9\_midsp\_2~X0~X1~X4~X3)){\unicdcdcdhd}(((k9\_midsp\_2~\\
X0~X1~X2~X5=k9\_midsp\_2~X0~X1~X4~X3){\unicdbdjdcd}(k3\_midsp\_1~X0~X2~X3=k3\_midsp\_1~\\
X0~X4~X5)){\unicdcdcdhd}(((k9\_midsp\_2~X0~X1~X2~X3=X6){\unicdbdjdcd}(k10\_midsp\_2~X0~X1~X2~X6=\\
X3)){\unicdcdcdhd}((k10\_midsp\_2~X0~X1~X2~X6=X3){\unicdbdjdcd}(k9\_midsp\_2~X0~X1~X2~X3=X6)))))))))))))))))))\end{array}
\label{hyp:ehddddpfngjgegdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_midsp\_3~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_2~X3~(u1\_struct\_0~X1)~(k4\_finseq\_2~(k2\_nat\_1~X0~np\_\_1)~\\
(u1\_struct\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_midsp\_2~X4~X1){\unicdcdcdhd}(l1\_midsp\_2~\\
X4~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_finseq\_2~X5~(u1\_struct\_0~(u1\_midsp\_2~\\
X1~X4))~(k4\_finseq\_2~(k2\_nat\_1~X0~np\_\_1)~(u1\_struct\_0~(u1\_midsp\_2~\\
X1~X4)))){\unicdbdjdcd}((k7\_midsp\_3~X0~X1~X4~X2~X5=X3){\unicdbdjdcd}(k10\_midsp\_3~X0~X1~X4~X5=\\
k9\_midsp\_2~X1~X4~X2~(k4\_midsp\_3~X0~X1~X2~X3))))))))\end{array}
\label{hyp:mgddjdpfngjgegdhahpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_midsp\_3~\\
X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_midsp\_1~X1){\unicdcdcdhd}(l1\_midsp\_3~X1~(k2\_nat\_1~\\
X0~np\_\_2)))))\end{array}
\label{hyp:egehpfngcdpfngjgegdhahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_midsp\_3~\\
X1~X0){\unicdbdjdcd}(l1\_midsp\_1~X1))\end{array}
\label{hyp:egehpfmgbdpfngjgegdhahpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(v7\_ordinal1~\\
X1)){\unicdbdjdcd}(m2\_subset\_1~(k2\_nat\_1~X0~X1)~k1\_numbers~k5\_numbers)\end{array}
\label{hyp:egehpflgcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfngjgegdhahpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_midsp\_3~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_2~X4~\\
(u1\_struct\_0~X1)~(k4\_finseq\_2~(k2\_nat\_1~X0~np\_\_1)~(u1\_struct\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v4\_midsp\_2~X5~X1){\unicdcdcdhd}(l1\_midsp\_2~X5~X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~(u1\_midsp\_2~X1~X5))){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m2\_finseq\_2~X7~(u1\_struct\_0~(u1\_midsp\_2~X1~X5))~(k4\_finseq\_2~\\
(k2\_nat\_1~X0~np\_\_1)~(u1\_struct\_0~(u1\_midsp\_2~X1~X5)))){\unicdbdjdcd}(((k7\_midsp\_3~\\
X0~X1~X5~X2~X7=X4){\unicdcdcdhd}((k10\_midsp\_2~X1~X5~X2~X6=X3){\unicdcdcdhd}(k4\_midsp\_3~X0~X1~\\
X2~X4=X3))){\unicdbdjdcd}(k10\_midsp\_3~X0~X1~X5~X7=X6)))))))))\end{array}$$
\end{theorem}
\end{document}
