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\begin{document}
\title{t21\_funcop\_1 (TMWi2KjBR7jec1BPqm3ie7RHkttGjgBwqaB)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}\\
(v1\_funct\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  (X3 \in k9\_xtuple\_0~(k3\_relat\_1~(k13\_funct\_3~\\
X0~X1)~X2)){\unicdbdjdcd}(k1\_funct\_1~(k3\_relat\_1~(k13\_funct\_3~X0~X1)~X2)~X3=\\
k1\_binop\_1~X2~(k1\_funct\_1~X0~X3)~(k1\_funct\_1~X1~X3)))))\end{array}
\label{hyp:mgcdedpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~\\
X0)){\unicdcdcdhd}(((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}(\\
v1\_funct\_1~X2)))){\unicdbdjdcd}((v1\_relat\_1~(k3\_funcop\_1~X0~X1~X2)){\unicdcdcdhd}(v1\_funct\_1~\\
(k3\_funcop\_1~X0~X1~X2)))\end{array}
\label{hyp:ggdgfdpfggfhogdgpgahpfbd}
\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}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}\\
(v1\_funct\_1~X2)){\unicdbdjdcd}(k3\_funcop\_1~X0~X1~X2=k3\_relat\_1~(k13\_funct\_3~\\
X1~X2)~X0)))\end{array}
\label{hyp:egddpfggfhogdgpgahpfbd}
\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}((X0=X1){\unicdbdjded}((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)))))\end{array}
\label{hyp:egbdbdpfggfhogdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfggfhogdgpgahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}\\
(v1\_funct\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}\\
(((k9\_xtuple\_0~X3=k9\_xtuple\_0~(k3\_funcop\_1~X2~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(X4 \in k9\_xtuple\_0~(k3\_funcop\_1~X2~X0~X1)){\unicdbdjdcd}(k1\_funct\_1~X3~X4=k1\_binop\_1~\\
X2~(k1\_funct\_1~X0~X4)~(k1\_funct\_1~X1~X4)))){\unicdbdjdcd}(X3=k3\_funcop\_1~X2~\\
X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
