\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{t36\_trees\_9 (TMNToxZ1VdSTnBpGJFaLDuwdLKR675Z8Ekx)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_9 : {{\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 $ k2\_trees\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_trees\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_trees\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\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}
\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 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))\end{array}
\label{hyp:egehpfngbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\\
v3\_trees\_2~X0){\unicdcdcdhd}(v3\_trees\_9~X0)))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))){\unicdbdjdcd}((v1\_relat\_1~(k2\_trees\_9~X0~X1)){\unicdcdcdhd}((\\
v1\_funct\_1~(k2\_trees\_9~X0~X1)){\unicdcdcdhd}(v1\_finseq\_1~(k2\_trees\_9~X0~X1))))\end{array}
\label{hyp:egehpflgcdpfehchfgfgdhpfjd}
\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){\unicdcdcdhd}\\
(v3\_trees\_9~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}((X1 \in k9\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\\
v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~X2))){\unicdbdjdcd}((X2=k2\_trees\_9~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_trees\_1~X3~(k9\_xtuple\_0~X0)){\unicdcdcdhd}((X3=X1){\unicdcdcdhd}\\
(X2=k3\_relat\_1~(k1\_trees\_9~(k9\_xtuple\_0~X0)~X3)~X0)))))))\end{array}
\label{hyp:eggdpfehchfgfgdhpfjd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfehchfgfgdhpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v3\_trees\_2~X0){\unicdcdcdhd}\\
(v3\_trees\_9~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_trees\_1~X1~(k9\_xtuple\_0~X0)){\unicdbdjdcd}\\
(k2\_trees\_9~X0~X1=k3\_relat\_1~(k1\_trees\_9~(k9\_xtuple\_0~X0)~X1)~\\
X0))\end{array}$$
\end{theorem}
\end{document}
