\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t19\_e\_siec (TMYK39vmP72rGgDaJnbi4XXcVVaaNoq9jv6)}
\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_relat\_1~X2){\unicdbdjdcd}((r1\_tarski~\\
X2~(k2\_zfmisc\_1~X0~X1)){\unicdbdjdcd}(r1\_tarski~(k2\_relat\_1~X2)~(k2\_zfmisc\_1~\\
X1~X0)))\end{array}
\label{hyp:ehedpfdhjhdhchfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k4\_xboole\_0~(k2\_xboole\_0~X0~\\
X1)~X2=k2\_xboole\_0~(k4\_xboole\_0~X0~X2)~(k4\_xboole\_0~X1~X2)\end{array}
\label{hyp:ehedcdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}(k2\_relat\_1~\\
(k6\_subset\_1~X0~X1)=k6\_subset\_1~(k2\_relat\_1~X0)~(k2\_relat\_1~X1)))\end{array}
\label{hyp:ehcdedpfchfgmgbgehpfbd}
\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~(k4\_xboole\_0~(u1\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~\\
X0)))~(k2\_zfmisc\_1~(k8\_e\_siec~X0)~(k7\_e\_siec~X0))){\unicdcdcdhd}(r1\_tarski~\\
(k4\_xboole\_0~(u2\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~X0)))~(k2\_zfmisc\_1~\\
(k8\_e\_siec~X0)~(k7\_e\_siec~X0))))\end{array}
\label{hyp:ehbdidpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}\\
(r1\_tarski~X2~X3)){\unicdbdjdcd}(r1\_tarski~(k2\_xboole\_0~X0~X2)~(k2\_xboole\_0~\\
X1~X3))\end{array}
\label{hyp:ehbdddpfihcgpgpgmgfgpfbd}
\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 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_relat\_1}~{({{k4\_relat\_1}~{X0}})}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chegddpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X0){\unicdbdjdcd}(v1\_relat\_1~(k4\_xboole\_0~\\
X0~X1))\end{array}
\label{hyp:ggdgcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_e\_siec}~{X0}})}{\unicdbdjdcd}{({{v1\_relat\_1}~{({{u1\_e\_siec}~{X0}})}})}}}\label{hyp:egehpffhbdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_e\_siec}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_relat\_1}~{({{k4\_relat\_1}~{X0}})}}}\label{hyp:egehpflgedpfchfgmgbgehpfbd}
\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\_struct\_0~X0){\unicdbdjdcd}(k3\_struct\_0~X0=k6\_partfun1~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egedpfdhehchfhdgehpfad}
\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}\\
(k9\_e\_siec~X0=k4\_xboole\_0~(k2\_xboole\_0~(k2\_relat\_1~(u1\_e\_siec~\\
X0))~(u2\_e\_siec~X0))~(k3\_struct\_0~X0))\end{array}
\label{hyp:egbdbdpffgpfdhjgfgdg}
\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:ehbdjdpffgpfdhjgfgdg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
(r1\_tarski~(k9\_e\_siec~X0)~(k2\_xboole\_0~(k2\_zfmisc\_1~(k7\_e\_siec~\\
X0)~(k8\_e\_siec~X0))~(k2\_zfmisc\_1~(k8\_e\_siec~X0)~(k7\_e\_siec~X0))))\end{array}$$
\end{theorem}
\end{document}
