\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{t26\_functor0 (TMXcicvShBv5LstkagBBomvnUgdeaMVFtSR)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_altcat\_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 $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k8\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k9\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v11\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v8\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v9\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v10\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}((k1\_altcat\_1~X1~X2~X2{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_altcat\_1~X1~X2~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_altcat\_1~X0~X4~X5)){\unicdbdjdcd}((k1\_altcat\_1~\\
X0~X4~X5{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}(k1\_funct\_1~(k4\_functor0~X0~X1~(k9\_functor0~\\
X0~X1~X2~X3)~X4~X5)~X6=X3)))))))))\end{array}
\label{hyp:ehcdedpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdcdcdhd}\\
(((v11\_functor0~X2~X0~X1){\unicdcdcdhd}(l2\_functor0~X2~X0~X1)){\unicdcdcdhd}((m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X4~(u1\_struct\_0~X0)))))){\unicdbdjdcd}(\\
k7\_functor0~X0~X1~X2~X3~X4=k4\_functor0~X0~X1~X2~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}\\
(l1\_altcat\_1~X1))){\unicdcdcdhd}((m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_altcat\_1~X1~X2~X2))))){\unicdbdjdcd}((v8\_functor0~(k9\_functor0~X0~X1~\\
X2~X3)~X0~X1){\unicdcdcdhd}((v9\_functor0~(k9\_functor0~X0~X1~X2~X3)~X0~X1){\unicdcdcdhd}((v10\_functor0~\\
(k9\_functor0~X0~X1~X2~X3)~X0~X1){\unicdcdcdhd}(v11\_functor0~(k9\_functor0~X0~X1~\\
X2~X3)~X0~X1))))\end{array}
\label{hyp:ggdggdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_altcat\_1~\\
X1~X2~X2))))){\unicdbdjdcd}((v9\_functor0~(k9\_functor0~X0~X1~X2~X3)~X0~X1){\unicdcdcdhd}(l2\_functor0~\\
(k9\_functor0~X0~X1~X2~X3)~X0~X1))\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdbdjdcd}((v1\_altcat\_2~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_altcat\_1~\\
X0~X1~X1{\unicdcdgdad}k1\_xboole\_0)))\end{array}
\label{hyp:eghdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v11\_functor0~\\
X2~X0~X1){\unicdcdcdhd}(l2\_functor0~X2~X0~X1)){\unicdbdjdcd}((v8\_functor0~X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (k1\_altcat\_1~X0~X3~X4{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k1\_altcat\_1~\\
X1~(k3\_functor0~X0~X1~X2~X4)~(k3\_functor0~X0~X1~X2~X3)=k1\_xboole\_0)))))))\end{array}
\label{hyp:egbdjdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v11\_functor0~\\
X2~X0~X1){\unicdcdcdhd}(l2\_functor0~X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(\\
u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(\preoh (k1\_altcat\_1~X0~X3~X4{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_altcat\_1~X1~(k3\_functor0~\\
X0~X1~X2~X4)~(k3\_functor0~X0~X1~X2~X3){\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(\preoh {\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(k1\_altcat\_1~X0~X3~X4)){\unicdbdjdcd}(k8\_functor0~X0~X1~X2~X3~\\
X4~X5=k1\_funct\_1~(k7\_functor0~X0~X1~X2~X3~X4)~X5))))))))\end{array}
\label{hyp:egbdgdpfggfhogdgehpgchad}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfggfhogdgehpgchad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}(l1\_altcat\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k1\_altcat\_1~X1~X2~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(k1\_altcat\_1~X0~X4~X5)){\unicdbdjdcd}((k1\_altcat\_1~X0~X4~X5{\unicdcdgdad}\\
k1\_xboole\_0){\unicdbdjdcd}(k8\_functor0~X0~X1~(k9\_functor0~X0~X1~X2~X3)~X4~X5~X6=\\
X3))))))))\end{array}$$
\end{theorem}
\end{document}
