\documentclass{article}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t16\_trees\_4 (TMUBstBEGzUP7BGaH8KwnbEZTXuVZMQNXVk)}
\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 $ k1\_trees\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_trees\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_trees\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k12\_finseq\_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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v1\_finseq\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v1\_finseq\_1~X3))){\unicdbdjdcd}((k3\_trees\_4~X0~X2=k3\_trees\_4~X1~X3){\unicdbdjdcd}\\
((X0=X1){\unicdcdcdhd}(X2=X3))))\end{array}
\label{hyp:ehhdpfehchfgfgdhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (k9\_xtuple\_0~(k1\_trees\_4~X0)=k2\_trees\_1~k6\_numbers){\unicdcdcdhd}\\
(k1\_funct\_1~(k1\_trees\_4~X0)~k1\_xboole\_0=X0)\end{array}
\label{hyp:ehddpfehchfgfgdhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(((k9\_xtuple\_0~X0=k9\_xtuple\_0~\\
X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}(k1\_funct\_1~X0~X2=k1\_funct\_1~\\
X1~X2))){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehcdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{k2\_trees\_1}~{k6\_numbers}}={{k1\_tarski}~{k1\_xboole\_0}}}\label{hyp:ehcdjdpfehchfgfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(k3\_finseq\_1~(k3\_finseq\_1~X0)=k3\_finseq\_1~X0)\end{array}
\label{hyp:ahchpgkgfgdgehjgghjgehjhpflgddpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
((X0=k1\_xboole\_0){\unicdbdjded}(k3\_finseq\_1~X0=k6\_numbers))\end{array}
\label{hyp:mgcdhdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\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~(k3\_trees\_4~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k3\_trees\_4~\\
X0~X1)){\unicdcdcdhd}(v3\_trees\_2~(k3\_trees\_4~X0~X1))))\end{array}
\label{hyp:egehpflgddpfehchfgfgdhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k1\_trees\_4~X0)){\unicdcdcdhd}((v1\_funct\_1~(k1\_trees\_4~\\
X0)){\unicdcdcdhd}(v3\_trees\_2~(k1\_trees\_4~X0)))\end{array}
\label{hyp:egehpflgbdpfehchfgfgdhpfed}
\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}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v3\_trees\_2~\\
X2))){\unicdbdjdcd}((X2=k3\_trees\_4~X0~X1){\unicdbdjded}((k9\_xtuple\_0~X2=k2\_trees\_1~(k3\_finseq\_1~\\
X1)){\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}(k1\_funct\_1~\\
X2~(k12\_finseq\_1~k5\_numbers~X3)=k1\_funct\_1~X1~(k2\_nat\_1~X3~np\_\_1))))))))\end{array}
\label{hyp:egddpfehchfgfgdhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_relat\_1}~{X0}})}}}\label{hyp:dgdgbdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_funct\_1}~{X0}})}}}\label{hyp:dgdgbdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_xboole\_0~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v1\_finseq\_1~X0))\end{array}
\label{hyp:dgdgbdpfggjgogdhfgbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfehchfgfgdhpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v1\_finseq\_1~X2))){\unicdbdjdcd}((k1\_trees\_4~X0=k3\_trees\_4~X1~X2){\unicdbdjdcd}((\\
X0=X1){\unicdcdcdhd}(X2=k1\_xboole\_0)))\end{array}$$
\end{theorem}
\end{document}
