\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{t17\_e\_siec (TMPokcwpKRaubhuTyvi7Xme4MU5kUDuob4a)}
\maketitle
Let $ v2\_e\_siec : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_e\_siec : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_e\_siec : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_sysrel : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 .  {\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 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_tarski~\\
(k4\_xboole\_0~X0~X2)~(k4\_xboole\_0~X1~X2))\end{array}
\label{hyp:ehddddpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_relat\_1~X2){\unicdbdjdcd}((((k3\_relat\_1~\\
X2~X2=X2){\unicdcdcdhd}((k3\_relat\_1~X2~(k6\_subset\_1~X2~(k4\_relat\_1~(k9\_xtuple\_0~\\
X2)))=k1\_xboole\_0){\unicdcdcdhd}(k4\_tarski~X0~X1 \in X2))){\unicdbdjdcd}((X0=X1){\unicdcdcdid}((X0 \in k6\_subset\_1~\\
(k9\_xtuple\_0~X2)~(k9\_xtuple\_0~(k1\_sysrel~X2))){\unicdcdcdhd}(X1 \in k9\_xtuple\_0~\\
(k1\_sysrel~X2))))){\unicdcdcdhd}(((k3\_relat\_1~X2~X2=X2){\unicdcdcdhd}((k3\_relat\_1~(k6\_subset\_1~\\
X2~(k4\_relat\_1~(k9\_xtuple\_0~X2)))~X2=k1\_xboole\_0){\unicdcdcdhd}(k4\_tarski~\\
X0~X1 \in X2))){\unicdbdjdcd}((X0=X1){\unicdcdcdid}((X1 \in k6\_subset\_1~(k10\_xtuple\_0~X2)~(k9\_xtuple\_0~\\
(k1\_sysrel~X2))){\unicdcdcdhd}(X0 \in k9\_xtuple\_0~(k1\_sysrel~X2))))))\end{array}
\label{hyp:ehddadpfdhjhdhchfgmg}
\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}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
((r1\_tarski~(k9\_xtuple\_0~(u1\_e\_siec~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
(r1\_tarski~(k10\_xtuple\_0~(u1\_e\_siec~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
(r1\_tarski~(k9\_xtuple\_0~(u2\_e\_siec~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(r1\_tarski~\\
(k10\_xtuple\_0~(u2\_e\_siec~X0))~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:ehbdedpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
((k10\_xtuple\_0~(u1\_e\_siec~X0)=k10\_xtuple\_0~(k1\_sysrel~(u1\_e\_siec~\\
X0))){\unicdcdcdhd}((k10\_xtuple\_0~(u1\_e\_siec~X0)=k9\_xtuple\_0~(k1\_sysrel~\\
(u1\_e\_siec~X0))){\unicdcdcdhd}((k10\_xtuple\_0~(u2\_e\_siec~X0)=k10\_xtuple\_0~\\
(k1\_sysrel~(u2\_e\_siec~X0))){\unicdcdcdhd}((k10\_xtuple\_0~(u2\_e\_siec~X0)=k9\_xtuple\_0~\\
(k1\_sysrel~(u2\_e\_siec~X0))){\unicdcdcdhd}(k10\_xtuple\_0~(u1\_e\_siec~X0)=k10\_xtuple\_0~\\
(u2\_e\_siec~X0))))))\end{array}
\label{hyp:ehbdddpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
((k4\_xboole\_0~(u1\_e\_siec~X0)~(k4\_relat\_1~(k9\_xtuple\_0~(u1\_e\_siec~\\
X0)))=k4\_xboole\_0~(u1\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}\\
((k4\_xboole\_0~(u2\_e\_siec~X0)~(k4\_relat\_1~(k9\_xtuple\_0~(u2\_e\_siec~\\
X0)))=k4\_xboole\_0~(u2\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}\\
((k4\_xboole\_0~(u1\_e\_siec~X0)~(k4\_relat\_1~(k10\_xtuple\_0~(u1\_e\_siec~\\
X0)))=k4\_xboole\_0~(u1\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}\\
(k4\_xboole\_0~(u2\_e\_siec~X0)~(k4\_relat\_1~(k10\_xtuple\_0~(u2\_e\_siec~\\
X0)))=k4\_xboole\_0~(u2\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:ehbdbdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k3\_relat\_1}~{X0}}~{X1}})}}}}\label{hyp:egehpflgddpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
(k7\_e\_siec~X0=k10\_xtuple\_0~(u1\_e\_siec~X0))\end{array}
\label{hyp:egjdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_e\_siec~X0){\unicdbdjdcd}((v3\_e\_siec~X0){\unicdbdjded}((k3\_relat\_1~(u1\_e\_siec~\\
X0)~(k4\_xboole\_0~(u1\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~X0)))=\\
k1\_xboole\_0){\unicdcdcdhd}(k3\_relat\_1~(u2\_e\_siec~X0)~(k4\_xboole\_0~(u2\_e\_siec~\\
X0)~(k4\_relat\_1~(u1\_struct\_0~X0)))=k1\_xboole\_0)))\end{array}
\label{hyp:egcdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_e\_siec~X0){\unicdbdjdcd}((v2\_e\_siec~X0){\unicdbdjded}((r1\_tarski~(u1\_e\_siec~\\
X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))){\unicdcdcdhd}((r1\_tarski~\\
(u2\_e\_siec~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))){\unicdcdcdhd}\\
((k3\_relat\_1~(u1\_e\_siec~X0)~(u1\_e\_siec~X0)=u1\_e\_siec~X0){\unicdcdcdhd}((k3\_relat\_1~\\
(u1\_e\_siec~X0)~(u2\_e\_siec~X0)=u1\_e\_siec~X0){\unicdcdcdhd}((k3\_relat\_1~(u2\_e\_siec~\\
X0)~(u2\_e\_siec~X0)=u2\_e\_siec~X0){\unicdcdcdhd}(k3\_relat\_1~(u2\_e\_siec~X0)~(\\
u1\_e\_siec~X0)=u2\_e\_siec~X0)))))))\end{array}
\label{hyp:egbdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
(k8\_e\_siec~X0=k4\_xboole\_0~(u1\_struct\_0~X0)~(k7\_e\_siec~X0))\end{array}
\label{hyp:egbdadpffgpfdhjgfgdg}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpffgpfdhjgfgdg}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v2\_e\_siec~X2){\unicdcdcdhd}((v3\_e\_siec~\\
X2){\unicdcdcdhd}(l1\_e\_siec~X2))){\unicdbdjdcd}(\preoh ((k4\_tarski~X0~X1 \in u1\_e\_siec~X2){\unicdcdcdid}(k4\_tarski~\\
X0~X1 \in u2\_e\_siec~X2)){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdcdcdhd}(\preoh (X0 \in k8\_e\_siec~X2){\unicdcdcdhd}(X1 \in k7\_e\_siec~\\
X2))))\end{array}$$
\end{theorem}
\end{document}
