\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\preoh[1]{\lnot #1}
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\begin{document}
\title{t12\_trees\_4 (TMcKcd61XE2hZHqS5DU3xxEqWCvhY8YYcqs)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_trees\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_trees\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_trees\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_trees\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_trees\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_trees\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_trees\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_trees\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_trees\_1~X1~X0){\unicdbdjded}(m1\_subset\_1~X1~X0))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngbdpfehchfgfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_trees\_2~X0))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k9\_xtuple\_0~X0)){\unicdcdcdhd}(v1\_trees\_1~(k9\_xtuple\_0~X0)))\end{array}
\label{hyp:ggdgcdpfehchfgfgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_trees\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_trees\_1~X1~X0){\unicdbdjdcd}(m2\_finseq\_1~X1~k5\_numbers))\end{array}
\label{hyp:egehpfngbdpfehchfgfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((v1\_relat\_1~(k4\_trees\_4~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k4\_trees\_4~\\
X0~X1)){\unicdcdcdhd}(v3\_trees\_2~(k4\_trees\_4~X0~X1))))\end{array}
\label{hyp:egehpflgedpfehchfgfgdhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(m2\_finseq\_1~(k12\_finseq\_1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgbdcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((v6\_trees\_3~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v3\_trees\_2~X2))){\unicdbdjdcd}((X2=k4\_trees\_4~X0~X1){\unicdbdjded}(({\unicdcdaddd} X3 .  (\\
(v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_finseq\_1~X3){\unicdcdcdhd}(v6\_trees\_3~\\
X3)))){\unicdcdcdhd}((X1=X3){\unicdcdcdhd}(k9\_xtuple\_0~X2=k11\_trees\_3~(k2\_funct\_6~X3)))){\unicdcdcdhd}\\
((k1\_funct\_1~X2~k1\_xboole\_0=X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
k5\_numbers){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X1)~X3){\unicdbdjdcd}(k5\_trees\_2~\\
X2~(k12\_finseq\_1~k5\_numbers~X3)=k1\_funct\_1~X1~(k2\_nat\_1~X3~np\_\_1)))))))))\end{array}
\label{hyp:egedpfehchfgfgdhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_trees\_2~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v3\_trees\_2~X2))){\unicdbdjdcd}((X2=k5\_trees\_2~X0~X1){\unicdbdjded}\\
((k9\_xtuple\_0~X2=k4\_trees\_1~(k9\_xtuple\_0~X0)~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_1~X3~k5\_numbers){\unicdbdjdcd}((X3 \in k4\_trees\_1~(k9\_xtuple\_0~X0)~\\
X1){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k1\_funct\_1~X0~(k8\_finseq\_1~k5\_numbers~X1~\\
X3))))))))\end{array}
\label{hyp:egbdadpfehchfgfgdhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfehchfgfgdhpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finseq\_1~\\
X1){\unicdcdcdhd}(v6\_trees\_3~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v3\_trees\_2~X3))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_trees\_1~X4~(k9\_xtuple\_0~X3)){\unicdbdjdcd}((X3=k1\_funct\_1~\\
X1~(k2\_nat\_1~X2~np\_\_1)){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X1)~X2){\unicdcdcdid}(k1\_funct\_1~\\
(k4\_trees\_4~X0~X1)~(k8\_finseq\_1~k5\_numbers~(k12\_finseq\_1~k5\_numbers~\\
X2)~X4)=k1\_funct\_1~X3~X4))))))\end{array}$$
\end{theorem}
\end{document}
