\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}
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\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t19\_yellow20 (TMFeS7SfG7hsLkeSHFjGiY7Yr1USn2qBE4t)}
\maketitle
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_yellow20 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_yellow20 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_altcat\_1 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_yellow20 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X1)){\unicdbdjdcd}(\\
(r1\_yellow20~X0~X1){\unicdbdjdcd}(r1\_yellow20~X1~X0))\end{array}
\label{hyp:dhjhngngfgehchjhpfchbdpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}(m2\_pboole~(u2\_altcat\_1~X0)~(k3\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(k3\_altcat\_1~\\
(u1\_struct\_0~X0)~(u1\_altcat\_1~X0)~(u1\_altcat\_1~X0))~(k2\_altcat\_1~\\
(u1\_struct\_0~X0)~(u1\_altcat\_1~X0)))\end{array}
\label{hyp:egehpffhcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_altcat\_1~X0){\unicdbdjdcd}((v1\_relat\_1~(u1\_altcat\_1~X0)){\unicdcdcdhd}\\
((v4\_relat\_1~(u1\_altcat\_1~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))){\unicdcdcdhd}((v1\_funct\_1~(u1\_altcat\_1~X0)){\unicdcdcdhd}(v1\_partfun1~\\
(u1\_altcat\_1~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhbdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_pboole~X3~X0~X1~X2){\unicdbdjdcd}((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~\\
X3~X0){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_partfun1~X3~X0)))))\end{array}
\label{hyp:egehpfngcdpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_altcat\_1}~{X0}})}}}\label{hyp:egehpfmgcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(k2\_zfmisc\_1~X0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(k2\_zfmisc\_1~\\
X0~X0))))){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(k2\_zfmisc\_1~X0~X0)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}((\\
v1\_relat\_1~(k3\_altcat\_1~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k3\_altcat\_1~\\
X0~X1~X2)~(k3\_zfmisc\_1~X0~X0~X0)){\unicdcdcdhd}((v1\_funct\_1~(k3\_altcat\_1~X0~X1~\\
X2)){\unicdcdcdhd}(v1\_partfun1~(k3\_altcat\_1~X0~X1~X2)~(k3\_zfmisc\_1~X0~X0~X0)))))\end{array}
\label{hyp:egehpflgddpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X1)){\unicdbdjdcd}(\\
(v6\_altcat\_1~(k2\_yellow20~X0~X1)){\unicdcdcdhd}(l2\_altcat\_1~(k2\_yellow20~\\
X0~X1)))\end{array}
\label{hyp:egehpflgcdpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(k2\_zfmisc\_1~\\
X0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(k2\_zfmisc\_1~X0~X0))))){\unicdbdjdcd}\\
((v1\_relat\_1~(k2\_altcat\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k2\_altcat\_1~\\
X0~X1)~(k3\_zfmisc\_1~X0~X0~X0)){\unicdcdcdhd}((v1\_funct\_1~(k2\_altcat\_1~X0~X1)){\unicdcdcdhd}\\
(v1\_partfun1~(k2\_altcat\_1~X0~X1)~(k3\_zfmisc\_1~X0~X0~X0)))))\end{array}
\label{hyp:egehpflgcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l2\_altcat\_1~X1){\unicdbdjdcd}((\\
r1\_yellow20~X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v6\_altcat\_1~X2){\unicdcdcdhd}(l2\_altcat\_1~\\
X2)){\unicdbdjdcd}((X2=k2\_yellow20~X0~X1){\unicdbdjded}((u1\_struct\_0~X2=k3\_xboole\_0~(\\
u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((u1\_altcat\_1~X2=k1\_yellow20~\\
(u1\_altcat\_1~X0)~(u1\_altcat\_1~X1)){\unicdcdcdhd}(u2\_altcat\_1~X2=k1\_yellow20~\\
(u2\_altcat\_1~X0)~(u2\_altcat\_1~X1))))))))\end{array}
\label{hyp:egddpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X1}}={{{k3\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdcdcdhd}((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}(k1\_yellow20~X0~X1=k1\_yellow20~\\
X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdpfjhfgmgmgpghhcdad}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfjhfgmgmgpghhcdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l2\_altcat\_1~X1){\unicdbdjdcd}((\\
r1\_yellow20~X0~X1){\unicdbdjdcd}(k2\_yellow20~X0~X1=k2\_yellow20~X1~X0)))\end{array}$$
\end{theorem}
\end{document}
