\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{t47\_ec\_pf\_1 (TMQdwAHemuKbwwqJsPS9faH6nAby7CUesja)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_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 $ k9\_int\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\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 $ k7\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1 \in \\
k2\_zfmisc\_1~X2~X3){\unicdbdjded}((X0 \in X2){\unicdcdcdhd}(X1 \in X3))\end{array}
\label{hyp:ehidhdpfkhggngjgdhdgpfbd}
\end{equation}
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 .  {\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}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~(k3\_zfmisc\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0)))~(k3\_ec\_pf\_1~(k9\_int\_3~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k3\_zfmisc\_1~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0)))~\\
(k3\_ec\_pf\_1~(k9\_int\_3~X0))){\unicdbdjdcd}((r1\_ec\_pf\_1~X0~X1~X2){\unicdbdjded}(k1\_domain\_1~\\
(k3\_ec\_pf\_1~(k9\_int\_3~X0))~(k3\_ec\_pf\_1~(k9\_int\_3~X0))~X1~X2 \in k7\_ec\_pf\_1~\\
X0))))\end{array}
\label{hyp:ehedgdpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k3\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X3~X1)))){\unicdbdjdcd}\\
(k1\_domain\_1~X0~X1~X2~X3=k4\_tarski~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~(k9\_int\_3~X0))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_ec\_pf\_1~\\
X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k6\_ec\_pf\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k3\_ec\_pf\_1~\\
(k9\_int\_3~X0)))))\end{array}
\label{hyp:egehpflggdpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  m1\_subset\_1~(k1\_eqrel\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))\end{array}
\label{hyp:egehpflgbdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k3\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(X3 \in X1)))\end{array}
\label{hyp:egedpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_eqrel\_1}~{X0}}={{{k2\_zfmisc\_1}~{X0}}~{X0}}}}\label{hyp:egbdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}(k8\_ec\_pf\_1~X0~X1~X2=k9\_subset\_1~\\
(k2\_zfmisc\_1~(k6\_ec\_pf\_1~X0~X1~X2)~(k6\_ec\_pf\_1~X0~X1~X2))~(k7\_ec\_pf\_1~\\
X0)~(k1\_eqrel\_1~(k6\_ec\_pf\_1~X0~X1~X2)))))\end{array}
\label{hyp:egbdcdpffgdgpfahggpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedhdpffgdgpfahggpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k3\_zfmisc\_1~\\
(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~\\
(k9\_int\_3~X0)))~(k3\_ec\_pf\_1~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~(k3\_zfmisc\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0)))~(k3\_ec\_pf\_1~(k9\_int\_3~X0))){\unicdbdjdcd}\\
(((X3 \in k6\_ec\_pf\_1~X0~X1~X2){\unicdcdcdhd}(X4 \in k6\_ec\_pf\_1~X0~X1~X2)){\unicdbdjdcd}((k4\_ec\_pf\_1~\\
X0~X1~X2=k4\_struct\_0~(k9\_int\_3~X0)){\unicdcdcdid}((r1\_ec\_pf\_1~X0~X3~X4){\unicdbdjded}(k1\_domain\_1~\\
(k3\_ec\_pf\_1~(k9\_int\_3~X0))~(k3\_ec\_pf\_1~(k9\_int\_3~X0))~X3~X4 \in k8\_ec\_pf\_1~\\
X0~X1~X2))))))))\end{array}$$
\end{theorem}
\end{document}
