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\begin{document}
\title{t18\_gfacirc2 (TMNijynAdxpibL52RFQD2RGt8yzSkgLU3rq)}
\maketitle
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k8\_margrel1 : {\iota}$ be given.
Let $ k5\_gfacirc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k25\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_gfacirc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k26\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_gfacirc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k21\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
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 $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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}((X1=k9\_finseq\_1~X0){\unicdbdjded}((k3\_finseq\_1~X1=np\_\_1){\unicdcdcdhd}(k1\_funct\_1~\\
X1~np\_\_1=X0)))\end{array}
\label{hyp:ehedadpfggjgogdhfgbhpfbd}
\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}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (X2=k4\_tarski~k1\_xboole\_0~(k1\_margrel1~k6\_margrel1~\\
(k4\_finseq\_2~k6\_numbers~k6\_margrel1)~k8\_margrel1)){\unicdbdjdcd}((k5\_gfacirc2~\\
np\_\_1~X0~X1=k2\_circcomb~(k5\_circcomb~(k1\_margrel1~k6\_margrel1~\\
(k4\_finseq\_2~k6\_numbers~k6\_margrel1)~k8\_margrel1)~k1\_xboole\_0)~\\
(k25\_gfacirc1~(k1\_funct\_1~X0~np\_\_1)~(k1\_funct\_1~X1~np\_\_1)~X2)){\unicdcdcdhd}\\
((k6\_gfacirc2~np\_\_1~X0~X1=k3\_circcomb~(k5\_circcomb~(k1\_margrel1~\\
k6\_margrel1~(k4\_finseq\_2~k6\_numbers~k6\_margrel1)~k8\_margrel1)~\\
k1\_xboole\_0)~(k25\_gfacirc1~(k1\_funct\_1~X0~np\_\_1)~(k1\_funct\_1~\\
X1~np\_\_1)~X2)~(k7\_circcomb~k1\_xboole\_0~k6\_margrel1~(k1\_margrel1~\\
k6\_margrel1~(k4\_finseq\_2~k6\_numbers~k6\_margrel1)~k8\_margrel1)~\\
k1\_xboole\_0)~(k26\_gfacirc1~(k1\_funct\_1~X0~np\_\_1)~(k1\_funct\_1~\\
X1~np\_\_1)~X2)){\unicdcdcdhd}(k7\_gfacirc2~np\_\_1~X0~X1=k21\_gfacirc1~(k1\_funct\_1~\\
X0~np\_\_1)~(k1\_funct\_1~X1~np\_\_1)~X2)))))\end{array}
\label{hyp:ehbdhdpfhgggbgdgjgchdgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_finseq\_1}~{X0}}={{k5\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_finseq\_1}~{({{k5\_finseq\_1}~{X0}})}}}\label{hyp:ggdghdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k9\_finseq\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k9\_finseq\_1~\\
X0))\end{array}
\label{hyp:egehpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfhgggbgdgjgchdgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k4\_tarski~k1\_xboole\_0~(\\
k1\_margrel1~k6\_margrel1~(k4\_finseq\_2~k6\_numbers~k6\_margrel1)~\\
k8\_margrel1)){\unicdbdjdcd}((k5\_gfacirc2~np\_\_1~(k9\_finseq\_1~X0)~(k9\_finseq\_1~\\
X1)=k2\_circcomb~(k5\_circcomb~(k1\_margrel1~k6\_margrel1~(k4\_finseq\_2~\\
k6\_numbers~k6\_margrel1)~k8\_margrel1)~k1\_xboole\_0)~(k25\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}((k6\_gfacirc2~np\_\_1~(k9\_finseq\_1~X0)~(k9\_finseq\_1~X1)=\\
k3\_circcomb~(k5\_circcomb~(k1\_margrel1~k6\_margrel1~(k4\_finseq\_2~\\
k6\_numbers~k6\_margrel1)~k8\_margrel1)~k1\_xboole\_0)~(k25\_gfacirc1~\\
X0~X1~X2)~(k7\_circcomb~k1\_xboole\_0~k6\_margrel1~(k1\_margrel1~k6\_margrel1~\\
(k4\_finseq\_2~k6\_numbers~k6\_margrel1)~k8\_margrel1)~k1\_xboole\_0)~\\
(k26\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}(k7\_gfacirc2~np\_\_1~(k9\_finseq\_1~X0)~(\\
k9\_finseq\_1~X1)=k21\_gfacirc1~X0~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
