\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}
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\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{t5\_functor1 (TMGtDBt9dPq2SP4zudHaQUTGRJmUy2GBuoQ)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v21\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_msualg\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v19\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v20\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v18\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v17\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_struct\_0~X0){\unicdcdcdhd}((l1\_struct\_0~\\
X1){\unicdcdcdhd}(l1\_functor0~X2~X0~X1))){\unicdbdjdcd}((v1\_funct\_1~(u1\_functor0~X0~X1~X2)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_functor0~X0~X1~X2)~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X1))){\unicdcdcdhd}(m1\_subset\_1~(u1\_functor0~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X1)))))))\end{array}
\label{hyp:egehpffhbdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_altcat\_1~X0){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (l2\_functor0~X2~X0~X1){\unicdbdjdcd}(l1\_functor0~X2~X0~X1))\end{array}
\label{hyp:egehpfmgcdpfggfhogdgehpgchad}
\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}
{{\unicdcdadad} X0 .  {{({{l1\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_struct\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l1\_functor0~X2~X0~X1){\unicdbdjdcd}((v5\_functor0~X2~X0~X1){\unicdbdjded}(v2\_funct\_2~(u1\_functor0~\\
X0~X1~X2)~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:eghdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_struct\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l1\_functor0~X2~X0~X1){\unicdbdjdcd}((v4\_functor0~X2~X0~X1){\unicdbdjded}(v2\_funct\_1~(u1\_functor0~\\
X0~X1~X2)))))\end{array}
\label{hyp:eggdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_altcat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l2\_functor0~X2~X0~X1){\unicdbdjdcd}((v21\_functor0~X2~X0~X1){\unicdbdjded}((v19\_functor0~\\
X2~X0~X1){\unicdcdcdhd}(v20\_functor0~X2~X0~X1)))))\end{array}
\label{hyp:egddfdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_altcat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l2\_functor0~X2~X0~X1){\unicdbdjdcd}((v20\_functor0~X2~X0~X1){\unicdbdjded}((v18\_functor0~\\
X2~X0~X1){\unicdcdcdhd}(v5\_functor0~X2~X0~X1)))))\end{array}
\label{hyp:egddedpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_altcat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l2\_functor0~X2~X0~X1){\unicdbdjdcd}((v19\_functor0~X2~X0~X1){\unicdbdjded}((v4\_functor0~\\
X2~X0~X1){\unicdcdcdhd}(v17\_functor0~X2~X0~X1)))))\end{array}
\label{hyp:egddddpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_altcat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l2\_functor0~X2~X0~X1){\unicdbdjdcd}((v17\_functor0~X2~X0~X1){\unicdbdjded}(v1\_msualg\_3~(\\
u2\_functor0~X0~X1~X2)))))\end{array}
\label{hyp:egddadpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v2\_funct\_1~X2){\unicdcdcdhd}(v2\_funct\_2~\\
X2~X1))){\unicdbdjdcd}((v1\_funct\_1~X2){\unicdcdcdhd}(v3\_funct\_2~X2~X0~X1)))\end{array}
\label{hyp:dgdggdpfggfhogdgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehfdpfggfhogdgehpgchbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (l2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}((v21\_functor0~X2~X0~X1){\unicdbdjdcd}((v3\_funct\_2~(u1\_functor0~X0~\\
X1~X2)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X1))){\unicdcdcdhd}(v1\_msualg\_3~(u2\_functor0~\\
X0~X1~X2))))))\end{array}$$
\end{theorem}
\end{document}
