\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{t33\_scmpds\_7 (TMXQHN7cMDrEiXQu9iQzo5UjDUr9mSwm5DC)}
\maketitle
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmpds\_2 : {\iota}$ be given.
Let $ v1\_int\_1 : {{\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 $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k2\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmpds\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~\\
X1){\unicdbdjdcd}((X1 \in k2\_afinsq\_1~X0){\unicdbdjded}(\preoh r1\_xxreal\_0~(k5\_card\_1~X0)~X1)))\end{array}
\label{hyp:ehgdgdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}\\
((v4\_relat\_1~X3~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X3~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_finset\_1~X3){\unicdcdcdhd}(v1\_afinsq\_1~X3))))))){\unicdbdjdcd}\\
(k5\_card\_1~(k1\_scmpds\_7~X0~X1~X2~X3)=k2\_nat\_1~(k5\_card\_1~X3)~np\_\_3))))\end{array}
\label{hyp:ehddcdpfdhdgngahegdhpfhd}
\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}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\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 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_ami\_2~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmpds\_2))){\unicdcdcdhd}((v1\_int\_1~X1){\unicdcdcdhd}\\
((m1\_subset\_1~X2~k5\_numbers){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_relat\_1~\\
X3){\unicdcdcdhd}((v4\_relat\_1~X3~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X3~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_finset\_1~X3){\unicdcdcdhd}(v1\_afinsq\_1~\\
X3)))))))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k1\_scmpds\_7~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_relat\_1~\\
(k1\_scmpds\_7~X0~X1~X2~X3)){\unicdcdcdhd}((v4\_relat\_1~(k1\_scmpds\_7~X0~X1~X2~X3)~\\
k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(k1\_scmpds\_7~X0~X1~X2~X3)~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~(k1\_scmpds\_7~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_finset\_1~\\
(k1\_scmpds\_7~X0~X1~X2~X3)){\unicdcdcdhd}(v1\_afinsq\_1~(k1\_scmpds\_7~X0~X1~X2~X3))))))))\end{array}
\label{hyp:egehpflgbdpfdhdgngahegdhpfhd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddddpfdhdgngahegdhpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_relat\_1~X4){\unicdcdcdhd}((v4\_relat\_1~\\
X4~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X4~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X4){\unicdcdcdhd}((v1\_finset\_1~X4){\unicdcdcdhd}(v1\_afinsq\_1~X4))))))){\unicdbdjdcd}(\\
(\preoh r1\_xxreal\_0~(k2\_nat\_1~(k5\_card\_1~X4)~np\_\_3)~X3){\unicdbdjded}(X3 \in k2\_afinsq\_1~\\
(k1\_scmpds\_7~X0~X1~X2~X4)))))))\end{array}$$
\end{theorem}
\end{document}
