\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{t7\_scmpds\_9 (TMEou9KJoit8Tzko7WF9WhgM6kopw35Xtnt)}
\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 $ k5\_numbers : {\iota}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_amistd\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k10\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v7\_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~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_ami\_2~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}((k1\_funct\_1~\\
(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~(k10\_scmpds\_2~X3~X1~X2)~X0)~(k4\_struct\_0~\\
k1\_scmpds\_2)=k4\_card\_1~(k5\_memstr\_0~np\_\_2~k1\_scmpds\_2~X0)){\unicdcdcdhd}\\
((k1\_funct\_1~(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~(k10\_scmpds\_2~X3~\\
X1~X2)~X0)~(k2\_scmpds\_2~(k1\_funct\_1~X0~X3)~X1)=X2){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
((v1\_ami\_2~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
((X4{\unicdcdgdad}k2\_scmpds\_2~(k1\_funct\_1~X0~X3)~X1){\unicdbdjdcd}(k1\_funct\_1~(k2\_extpro\_1~\\
np\_\_2~k1\_scmpds\_2~(k10\_scmpds\_2~X3~X1~X2)~X0)~X4=k1\_funct\_1~X0~X4))))))))\end{array}
\label{hyp:ehedgdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}(({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(\\
(v4\_relat\_1~X2~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~\\
X2~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}((k5\_memstr\_0~np\_\_2~k1\_scmpds\_2~\\
X2=X1){\unicdbdjdcd}(k1\_funct\_1~(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~X0~X2)~(k4\_struct\_0~\\
k1\_scmpds\_2)=k1\_ordinal1~(k5\_memstr\_0~np\_\_2~k1\_scmpds\_2~X2)))){\unicdbdjdcd}\\
(k1\_amistd\_1~np\_\_2~k1\_scmpds\_2~X1~X0=k1\_tarski~(k1\_ordinal1~X1))))\end{array}
\label{hyp:ehbdpfdhdgngahegdhpfjd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k4\_card\_1}~{X0}}={{k1\_ordinal1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(u1\_struct\_0~k1\_scmpds\_2))){\unicdcdcdhd}((v1\_int\_1~X1){\unicdcdcdhd}(v1\_int\_1~X2))){\unicdbdjdcd}\\
(m1\_subset\_1~(k10\_scmpds\_2~X0~X1~X2)~(u1\_compos\_1~k1\_scmpds\_2))\end{array}
\label{hyp:egehpflgbdadpfdhdgngahegdhpfcd}
\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:ehhdpfdhdgngahegdhpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_int\_1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(k1\_amistd\_1~np\_\_2~k1\_scmpds\_2~\\
X1~(k10\_scmpds\_2~X0~X2~X3)=k1\_tarski~(k1\_ordinal1~X1)))))\end{array}$$
\end{theorem}
\end{document}
