\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t3\_gfacirc1 (TMTpWRgXkt89gnc9bqscegCM1YkE11PwrBS)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_gfacirc1 : {\iota}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_twoscomp : {\iota}$ be given.
Let $ k12\_twoscomp : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_twoscomp : {\iota}$ be given.
Let $ k4\_twoscomp : {\iota}$ be given.
Let $ k13\_twoscomp : {\iota}$ be given.
Let $ k11\_twoscomp : {\iota}$ be given.
Let $ k8\_margrel1 : {\iota}$ be given.
Let $ k2\_xboolean : {\iota}$ be given.
Let $ k7\_margrel1 : {\iota}$ be given.
Let $ k1\_xboolean : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_funct\_1~k2\_twoscomp~(k10\_finseq\_1~k6\_numbers~k6\_numbers)=\\
k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k2\_twoscomp~(k10\_finseq\_1~k6\_numbers~\\
np\_\_1)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k2\_twoscomp~(k10\_finseq\_1~\\
np\_\_1~k6\_numbers)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k2\_twoscomp~(k10\_finseq\_1~\\
np\_\_1~np\_\_1)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k3\_twoscomp~(k10\_finseq\_1~\\
k6\_numbers~k6\_numbers)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k3\_twoscomp~\\
(k10\_finseq\_1~k6\_numbers~np\_\_1)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k3\_twoscomp~\\
(k10\_finseq\_1~np\_\_1~k6\_numbers)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k3\_twoscomp~\\
(k10\_finseq\_1~np\_\_1~np\_\_1)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k4\_twoscomp~\\
(k10\_finseq\_1~k6\_numbers~k6\_numbers)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k4\_twoscomp~\\
(k10\_finseq\_1~k6\_numbers~np\_\_1)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k4\_twoscomp~\\
(k10\_finseq\_1~np\_\_1~k6\_numbers)=k6\_numbers){\unicdcdcdhd}(k1\_funct\_1~k4\_twoscomp~\\
(k10\_finseq\_1~np\_\_1~np\_\_1)=k6\_numbers)))))))))))\end{array}
\label{hyp:ehjdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k6\_margrel1){\unicdbdjdcd}((k1\_funct\_1~k2\_twoscomp~(k10\_finseq\_1~X0~X1)=\\
k1\_funct\_1~k13\_twoscomp~(k10\_finseq\_1~X0~X1)){\unicdcdcdhd}((k1\_funct\_1~k3\_twoscomp~\\
(k10\_finseq\_1~X0~X1)=k1\_funct\_1~k12\_twoscomp~(k10\_finseq\_1~X1~\\
X0)){\unicdcdcdhd}(k1\_funct\_1~k4\_twoscomp~(k10\_finseq\_1~X0~X1)=k1\_funct\_1~\\
k11\_twoscomp~(k10\_finseq\_1~X0~X1)))))\end{array}
\label{hyp:ehgdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k6\_margrel1){\unicdbdjdcd}((k1\_funct\_1~k2\_twoscomp~(k10\_finseq\_1~X0~X1)=\\
k10\_margrel1~X0~X1){\unicdcdcdhd}((k1\_funct\_1~k3\_twoscomp~(k10\_finseq\_1~X0~\\
X1)=k10\_margrel1~(k9\_margrel1~X0)~X1){\unicdcdcdhd}(k1\_funct\_1~k4\_twoscomp~\\
(k10\_finseq\_1~X0~X1)=k10\_margrel1~(k9\_margrel1~X0)~(k9\_margrel1~\\
X1)))))\end{array}
\label{hyp:ehbdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
{{k8\_margrel1}={k2\_xboolean}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k7\_margrel1}={k1\_xboolean}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k6\_margrel1)){\unicdbdjdcd}(k10\_margrel1~X0~X0=X0)\end{array}
\label{hyp:jgegfgngahpgehfgogdgfgpflgbdadpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_margrel1){\unicdbdjdcd}(m1\_subset\_1~(k9\_margrel1~\\
X0)~k6\_margrel1)\end{array}
\label{hyp:egehpflgjdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k8\_margrel1}}~{k6\_margrel1}}\label{hyp:egehpflgidpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k7\_margrel1}}~{k6\_margrel1}}\label{hyp:egehpflghdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k12\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k12\_twoscomp~(k4\_finseq\_2~\\
np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k12\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgbdcdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k4\_finseq\_2~np\_\_2~\\
k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}((X0=k3\_gfacirc1){\unicdbdjded}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k6\_margrel1){\unicdbdjdcd}(k1\_funct\_1~X0~(k10\_finseq\_1~X1~X2)=k10\_margrel1~\\
X1~(k9\_margrel1~X2)))))\end{array}
\label{hyp:egddpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_xboolean}={np\_\_1}}\label{hyp:egcdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xboolean}={k6\_numbers}}\label{hyp:egbdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k6\_margrel1)){\unicdbdjdcd}(k10\_margrel1~X0~X1=k10\_margrel1~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdadpfngbgchhgchfgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehddpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k6\_margrel1){\unicdbdjdcd}((k1\_funct\_1~k3\_gfacirc1~(k10\_finseq\_1~X0~X1)=\\
k10\_margrel1~X0~(k9\_margrel1~X1)){\unicdcdcdhd}((k1\_funct\_1~k3\_gfacirc1~(\\
k10\_finseq\_1~X0~X1)=k1\_funct\_1~k3\_twoscomp~(k10\_finseq\_1~X1~X0)){\unicdcdcdhd}\\
((k1\_funct\_1~k3\_gfacirc1~(k10\_finseq\_1~X0~X1)=k1\_funct\_1~k12\_twoscomp~\\
(k10\_finseq\_1~X0~X1)){\unicdcdcdhd}((k1\_funct\_1~k3\_gfacirc1~(k10\_finseq\_1~\\
k6\_numbers~k6\_numbers)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k3\_gfacirc1~\\
(k10\_finseq\_1~k6\_numbers~np\_\_1)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k3\_gfacirc1~\\
(k10\_finseq\_1~np\_\_1~k6\_numbers)=np\_\_1){\unicdcdcdhd}(k1\_funct\_1~k3\_gfacirc1~\\
(k10\_finseq\_1~np\_\_1~np\_\_1)=k6\_numbers))))))))\end{array}$$
\end{theorem}
\end{document}
