\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t29\_ftacell1 (TMGhpED16r484sYx2HGy9wQdQER3aKQME9i)}
\maketitle
Let $ v1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k36\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_twoscomp : {\iota}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k37\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_ftacell1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k14\_ftacell1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k17\_ftacell1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_ftacell1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k24\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k21\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xtuple\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_xtuple\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  \preoh (X4{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X3~(k36\_gfacirc1~X0~\\
X1~X2))~k2\_twoscomp){\unicdcdcdhd}((\preoh X4 \in k3\_msafree2~(k37\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(k4\_card\_3~(u3\_msualg\_1~(k13\_ftacell1~\\
X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~X3~X4)))){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~\\
X6~k6\_margrel1){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~k6\_margrel1){\unicdcdcdhd}({\unicdcdaddd} X8 .  \\
(m1\_subset\_1~X8~k6\_margrel1){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~k6\_margrel1){\unicdcdcdhd}\\
({\unicdcdaddd} X10 .  (m1\_subset\_1~X10~k6\_margrel1){\unicdcdcdhd}((X6=k1\_funct\_1~\\
X5~X0){\unicdcdcdhd}((X7=k1\_funct\_1~X5~X1){\unicdcdcdhd}((X8=k1\_funct\_1~X5~X2){\unicdcdcdhd}((X9=k1\_funct\_1~\\
X5~X3){\unicdcdcdhd}((X10=k1\_funct\_1~X5~X4){\unicdcdcdhd}(\preoh (k1\_funct\_1~(k5\_facirc\_1~(k13\_ftacell1~\\
X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~X3~X4)~X5~np\_\_4)~(k24\_gfacirc1~\\
(k36\_gfacirc1~X0~X1~X2)~X4~X3)=k9\_margrel1~(k2\_binarith~(k2\_binarith~\\
(k2\_binarith~(k2\_binarith~(k9\_margrel1~X6)~X7)~(k9\_margrel1~X8))~\\
X9)~(k9\_margrel1~X10))){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(k13\_ftacell1~\\
X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~X3~X4)~X5~np\_\_4)~X0=X6){\unicdcdcdhd}((k1\_funct\_1~\\
(k5\_facirc\_1~(k13\_ftacell1~X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~\\
X3~X4)~X5~np\_\_4)~X1=X7){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(k13\_ftacell1~\\
X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~X3~X4)~X5~np\_\_4)~X2=X8){\unicdcdcdhd}((k1\_funct\_1~\\
(k5\_facirc\_1~(k13\_ftacell1~X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~\\
X3~X4)~X5~np\_\_4)~X3=X9){\unicdcdcdhd}(k1\_funct\_1~(k5\_facirc\_1~(k13\_ftacell1~\\
X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~X3~X4)~X5~np\_\_4)~X4=X10))))))))))))))))))))))\end{array}
\label{hyp:mghdgdpfggehbgdgfgmgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xtuple\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_xtuple\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  \preoh (X4{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X3~(k36\_gfacirc1~X0~\\
X1~X2))~k2\_twoscomp){\unicdcdcdhd}((\preoh X4 \in k3\_msafree2~(k37\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(k4\_card\_3~(u3\_msualg\_1~(k13\_ftacell1~\\
X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~X3~X4)))){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~\\
X6~k6\_margrel1){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~k6\_margrel1){\unicdcdcdhd}({\unicdcdaddd} X8 .  \\
(m1\_subset\_1~X8~k6\_margrel1){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~k6\_margrel1){\unicdcdcdhd}\\
({\unicdcdaddd} X10 .  (m1\_subset\_1~X10~k6\_margrel1){\unicdcdcdhd}((X6=k1\_funct\_1~\\
X5~X0){\unicdcdcdhd}((X7=k1\_funct\_1~X5~X1){\unicdcdcdhd}((X8=k1\_funct\_1~X5~X2){\unicdcdcdhd}((X9=k1\_funct\_1~\\
X5~X3){\unicdcdcdhd}((X10=k1\_funct\_1~X5~X4){\unicdcdcdhd}(\preoh (k1\_funct\_1~(k5\_facirc\_1~(k13\_ftacell1~\\
X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~X3~X4)~X5~np\_\_4)~(k21\_gfacirc1~\\
(k36\_gfacirc1~X0~X1~X2)~X4~X3)=k1\_binarith~(k1\_binarith~(k10\_margrel1~\\
(k2\_binarith~(k2\_binarith~(k9\_margrel1~X6)~X7)~(k9\_margrel1~X8))~\\
(k9\_margrel1~X10))~(k10\_margrel1~(k9\_margrel1~X10)~X9))~(k10\_margrel1~\\
X9~(k2\_binarith~(k2\_binarith~(k9\_margrel1~X6)~X7)~(k9\_margrel1~\\
X8)))){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(k13\_ftacell1~X0~X1~X2~X3~X4)~\\
(k14\_ftacell1~X0~X1~X2~X3~X4)~X5~np\_\_4)~X0=X6){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~\\
(k13\_ftacell1~X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~X3~X4)~X5~np\_\_4)~\\
X1=X7){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(k13\_ftacell1~X0~X1~X2~X3~X4)~\\
(k14\_ftacell1~X0~X1~X2~X3~X4)~X5~np\_\_4)~X2=X8){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~\\
(k13\_ftacell1~X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~X3~X4)~X5~np\_\_4)~\\
X3=X9){\unicdcdcdhd}(k1\_funct\_1~(k5\_facirc\_1~(k13\_ftacell1~X0~X1~X2~X3~X4)~(\\
k14\_ftacell1~X0~X1~X2~X3~X4)~X5~np\_\_4)~X4=X10))))))))))))))))))))))\end{array}
\label{hyp:mghdfdpfggehbgdgfgmgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k18\_ftacell1~\\
X0~X1~X2~X3~X4=k24\_gfacirc1~(k36\_gfacirc1~X0~X1~X2)~X4~X3\end{array}
\label{hyp:egbdidpfggehbgdgfgmgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k17\_ftacell1~\\
X0~X1~X2~X3~X4=k21\_gfacirc1~(k36\_gfacirc1~X0~X1~X2)~X4~X3\end{array}
\label{hyp:egbdhdpfggehbgdgfgmgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfggehbgdgfgmgmgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xtuple\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_xtuple\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  \preoh (X4{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X3~(k36\_gfacirc1~X0~\\
X1~X2))~k2\_twoscomp){\unicdcdcdhd}((\preoh X4 \in k3\_msafree2~(k37\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(k4\_card\_3~(u3\_msualg\_1~(k13\_ftacell1~\\
X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~X3~X4)))){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~\\
X6~k6\_margrel1){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~k6\_margrel1){\unicdcdcdhd}({\unicdcdaddd} X8 .  \\
(m1\_subset\_1~X8~k6\_margrel1){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~k6\_margrel1){\unicdcdcdhd}\\
({\unicdcdaddd} X10 .  (m1\_subset\_1~X10~k6\_margrel1){\unicdcdcdhd}((X6=k1\_funct\_1~\\
X5~X0){\unicdcdcdhd}((X7=k1\_funct\_1~X5~X1){\unicdcdcdhd}((X8=k1\_funct\_1~X5~X2){\unicdcdcdhd}((X9=k1\_funct\_1~\\
X5~X3){\unicdcdcdhd}((X10=k1\_funct\_1~X5~X4){\unicdcdcdhd}(\preoh (k1\_funct\_1~(k5\_facirc\_1~(k13\_ftacell1~\\
X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~X3~X4)~X5~np\_\_4)~(k17\_ftacell1~\\
X0~X1~X2~X3~X4)=k1\_binarith~(k1\_binarith~(k10\_margrel1~(k2\_binarith~\\
(k2\_binarith~(k9\_margrel1~X6)~X7)~(k9\_margrel1~X8))~(k9\_margrel1~\\
X10))~(k10\_margrel1~(k9\_margrel1~X10)~X9))~(k10\_margrel1~X9~(k2\_binarith~\\
(k2\_binarith~(k9\_margrel1~X6)~X7)~(k9\_margrel1~X8)))){\unicdcdcdhd}(k1\_funct\_1~\\
(k5\_facirc\_1~(k13\_ftacell1~X0~X1~X2~X3~X4)~(k14\_ftacell1~X0~X1~X2~\\
X3~X4)~X5~np\_\_4)~(k18\_ftacell1~X0~X1~X2~X3~X4)=k9\_margrel1~(k2\_binarith~\\
(k2\_binarith~(k2\_binarith~(k2\_binarith~(k9\_margrel1~X6)~X7)~(\\
k9\_margrel1~X8))~X9)~(k9\_margrel1~X10))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
