\documentclass{article}
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\newtheorem{definition}{Definition}
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\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t2\_bintree1 (TMarsVJYXzqU8tGgxSvRYhZVfg4Uwsyfsjh)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k14\_trees\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_bintree1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v3\_trees\_2~X1))){\unicdbdjdcd}\\
(k14\_trees\_3~(k10\_finseq\_1~X0~X1)=k10\_finseq\_1~(k1\_funct\_1~X0~\\
k1\_xboole\_0)~(k1\_funct\_1~X1~k1\_xboole\_0)))\end{array}
\label{hyp:ehgdpfegehdgpgogdhehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k4\_pre\_poly~X0~X1~X2=k10\_finseq\_1~\\
X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v5\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v3\_trees\_2~X1))))){\unicdbdjdcd}(m1\_subset\_1~\\
(k1\_bintree1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgbdpfcgjgogehchfgfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v5\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v3\_trees\_2~X1)))){\unicdbdjdcd}(k1\_bintree1~\\
X0~X1=k1\_funct\_1~X1~k1\_xboole\_0))\end{array}
\label{hyp:egbdpfcgjgogehchfgfgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfcgjgogehchfgfgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v5\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v3\_trees\_2~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v3\_trees\_2~\\
X2)))){\unicdbdjdcd}(k14\_trees\_3~(k10\_finseq\_1~X1~X2)=k4\_pre\_poly~X0~(k1\_bintree1~\\
X0~X1)~(k1\_bintree1~X0~X2))))\end{array}$$
\end{theorem}
\end{document}
