\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t10\_trees\_a (TMNvK8ZvjonYjWzzfx29EQTixPZh6EddeHy)}
\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 $ m4\_trees\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k3\_trees\_a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_trees\_a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v3\_trees\_2~X0))){\unicdcdcdhd}((m4\_trees\_1~X1~(k9\_xtuple\_0~X0)){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v3\_trees\_2~X2))))){\unicdbdjdcd}((v1\_relat\_1~(k3\_trees\_a~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_1~(k3\_trees\_a~X0~X1~X2)){\unicdcdcdhd}(v3\_trees\_2~(k3\_trees\_a~\\
X0~X1~X2))))\end{array}
\label{hyp:egehpflgddpfehchfgfgdhpfbg}
\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 .  (m4\_trees\_1~X1~(k9\_xtuple\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v3\_trees\_2~X2))){\unicdbdjdcd}((X1{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v3\_trees\_2~X3))){\unicdbdjdcd}\\
((X3=k3\_trees\_a~X0~X1~X2){\unicdbdjded}((k9\_xtuple\_0~X3=k1\_trees\_a~(k9\_xtuple\_0~\\
X0)~(k9\_xtuple\_0~X2)~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_finseq\_1~X4~k5\_numbers){\unicdbdjdcd}\\
(\preoh (X4 \in k1\_trees\_a~(k9\_xtuple\_0~X0)~(k9\_xtuple\_0~X2)~X1){\unicdcdcdhd}(({\unicdcdaddd} X5 .  \\
(m2\_finseq\_1~X5~k5\_numbers){\unicdcdcdhd}((X5 \in X1){\unicdcdcdhd}(\preoh (\preoh r1\_tarski~X5~X4){\unicdcdcdhd}(\\
k1\_funct\_1~X3~X4=k1\_funct\_1~X0~X4)))){\unicdcdcdhd}({\unicdcdadad} X5 .  (m2\_finseq\_1~\\
X5~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_finseq\_1~X6~k5\_numbers){\unicdbdjdcd}(\preoh (X5 \in \\
X1){\unicdcdcdhd}((X6 \in k9\_xtuple\_0~X2){\unicdcdcdhd}((X4=k8\_finseq\_1~k5\_numbers~X5~X6){\unicdcdcdhd}\\
(k1\_funct\_1~X3~X4=k1\_funct\_1~X2~X6)))))))))))))))\end{array}
\label{hyp:egcdpfehchfgfgdhpfbg}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfehchfgfgdhpfbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_trees\_2~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v3\_trees\_2~X1))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m4\_trees\_1~X2~(k9\_xtuple\_0~X0)){\unicdbdjdcd}((X2{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~k5\_numbers){\unicdbdjdcd}(\preoh (X3 \in k9\_xtuple\_0~(\\
k3\_trees\_a~X0~X2~X1)){\unicdcdcdhd}(({\unicdcdaddd} X4 .  (m2\_finseq\_1~X4~k5\_numbers){\unicdcdcdhd}\\
((X4 \in X2){\unicdcdcdhd}(\preoh (\preoh r1\_tarski~X4~X3){\unicdcdcdhd}(k1\_funct\_1~(k3\_trees\_a~X0~X2~X1)~\\
X3=k1\_funct\_1~X0~X3)))){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_finseq\_1~X4~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m2\_finseq\_1~X5~k5\_numbers){\unicdbdjdcd}(\preoh (X4 \in X2){\unicdcdcdhd}((X5 \in k9\_xtuple\_0~\\
X1){\unicdcdcdhd}((X3=k8\_finseq\_1~k5\_numbers~X4~X5){\unicdcdcdhd}(k1\_funct\_1~(k3\_trees\_a~\\
X0~X2~X1)~X3=k1\_funct\_1~X1~X5))))))))))))\end{array}$$
\end{theorem}
\end{document}
