\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{t4\_gfacirc1 (TMcYXfRQWfA7UbcXc3mTbRPpyjSWxk6dTVf)}
\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 $ k4\_gfacirc1 : {\iota}$ be given.
Let $ k10\_finseq\_1 : {{\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 $ k15\_twoscomp : {\iota}$ be given.
Let $ k8\_twoscomp : {\iota}$ be given.
Let $ k4\_twoscomp : {\iota}$ be given.
Let $ k2\_twoscomp : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_twoscomp : {\iota}$ be given.
Let $ k13\_twoscomp : {\iota}$ be given.
Let $ k12\_twoscomp : {\iota}$ be given.
Let $ k11\_twoscomp : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k14\_twoscomp : {\iota}$ be given.
Let $ k16\_twoscomp : {\iota}$ be given.
Let $ k1\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_twoscomp : {\iota}$ be given.
Let $ k10\_twoscomp : {\iota}$ be given.
Let $ k10\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_0 : {\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}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\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~k14\_twoscomp~(k10\_finseq\_1~X0~X1)=\\
k2\_binarith~X0~X1){\unicdcdcdhd}((k1\_funct\_1~k15\_twoscomp~(k10\_finseq\_1~X0~\\
X1)=k2\_binarith~(k9\_margrel1~X0)~X1){\unicdcdcdhd}(k1\_funct\_1~k16\_twoscomp~\\
(k10\_finseq\_1~X0~X1)=k2\_binarith~(k9\_margrel1~X0)~(k9\_margrel1~\\
X1)))))\end{array}
\label{hyp:ehfdpfehhhpgdhdgpgngah}
\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~k8\_twoscomp~(k10\_finseq\_1~X0~X1)=\\
k1\_binarith~X0~X1){\unicdcdcdhd}((k1\_funct\_1~k9\_twoscomp~(k10\_finseq\_1~X0~\\
X1)=k1\_binarith~(k9\_margrel1~X0)~X1){\unicdcdcdhd}(k1\_funct\_1~k10\_twoscomp~\\
(k10\_finseq\_1~X0~X1)=k1\_binarith~(k9\_margrel1~X0)~(k9\_margrel1~\\
X1)))))\end{array}
\label{hyp:ehddpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k10\_xtuple\_0~(k10\_finseq\_1~X0~X1)=k2\_tarski~\\
X0~X1\end{array}
\label{hyp:ehbdcdhdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_funct\_1~k14\_twoscomp~(k10\_finseq\_1~k6\_numbers~k6\_numbers)=\\
k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k14\_twoscomp~(k10\_finseq\_1~k6\_numbers~\\
np\_\_1)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k14\_twoscomp~(k10\_finseq\_1~np\_\_1~\\
k6\_numbers)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k14\_twoscomp~(k10\_finseq\_1~\\
np\_\_1~np\_\_1)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k15\_twoscomp~(k10\_finseq\_1~\\
k6\_numbers~k6\_numbers)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k15\_twoscomp~(k10\_finseq\_1~\\
k6\_numbers~np\_\_1)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k15\_twoscomp~(k10\_finseq\_1~\\
np\_\_1~k6\_numbers)=k6\_numbers){\unicdcdcdhd}(k1\_funct\_1~k15\_twoscomp~(k10\_finseq\_1~\\
np\_\_1~np\_\_1)=np\_\_1)))))))\end{array}
\label{hyp:ehbdbdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_funct\_1~k8\_twoscomp~(k10\_finseq\_1~k6\_numbers~k6\_numbers)=\\
k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k8\_twoscomp~(k10\_finseq\_1~k6\_numbers~\\
np\_\_1)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k8\_twoscomp~(k10\_finseq\_1~np\_\_1~\\
k6\_numbers)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k8\_twoscomp~(k10\_finseq\_1~\\
np\_\_1~np\_\_1)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k9\_twoscomp~(k10\_finseq\_1~\\
k6\_numbers~k6\_numbers)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k9\_twoscomp~(k10\_finseq\_1~\\
k6\_numbers~np\_\_1)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k9\_twoscomp~(k10\_finseq\_1~\\
np\_\_1~k6\_numbers)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k9\_twoscomp~(k10\_finseq\_1~\\
np\_\_1~np\_\_1)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k10\_twoscomp~(k10\_finseq\_1~\\
k6\_numbers~k6\_numbers)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k10\_twoscomp~(k10\_finseq\_1~\\
k6\_numbers~np\_\_1)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k10\_twoscomp~(k10\_finseq\_1~\\
np\_\_1~k6\_numbers)=np\_\_1){\unicdcdcdhd}(k1\_funct\_1~k10\_twoscomp~(k10\_finseq\_1~\\
np\_\_1~np\_\_1)=k6\_numbers)))))))))))\end{array}
\label{hyp:ehbdadpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_margrel1){\unicdbdjdcd}(k9\_margrel1~(k9\_margrel1~\\
X0)=X0)\end{array}
\label{hyp:jgogghpgmgfhehjgghfgogfgdhdhpflgjdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k6\_margrel1}}}}\label{hyp:ggdgcdpfngbgchhgchfgmgbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k6\_margrel1)){\unicdbdjdcd}(m1\_subset\_1~(k2\_binarith~X0~X1)~k6\_margrel1)\end{array}
\label{hyp:egehpflgcdpfcgjgogbgchjgehig}
\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}(m1\_subset\_1~(k1\_binarith~X0~X1)~k6\_margrel1)\end{array}
\label{hyp:egehpflgbdpfcgjgogbgchjgehig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k15\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k15\_twoscomp~(k4\_finseq\_2~\\
np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k15\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgbdfdpfehhhpgdhdgpgngah}
\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=k4\_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)=k2\_binarith~\\
X1~(k9\_margrel1~X2)))))\end{array}
\label{hyp:egedpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3=X0){\unicdcdcdid}(X3=X1)))\end{array}
\label{hyp:egcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_margrel1}={{{k2\_tarski}~{k6\_numbers}}~{np\_\_1}}}\label{hyp:egbdbdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\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}(k2\_binarith~X0~X1=k2\_binarith~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfcgjgogbgchjgehig}
\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:ehedpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k6\_margrel1){\unicdbdjdcd}((k1\_funct\_1~k4\_gfacirc1~(k10\_finseq\_1~X0~X1)=\\
k2\_binarith~X0~(k9\_margrel1~X1)){\unicdcdcdhd}((k1\_funct\_1~k4\_gfacirc1~(k10\_finseq\_1~\\
X0~X1)=k1\_funct\_1~k15\_twoscomp~(k10\_finseq\_1~X0~X1)){\unicdcdcdhd}((k1\_funct\_1~\\
k4\_gfacirc1~(k10\_finseq\_1~X0~X1)=k1\_funct\_1~k8\_twoscomp~(k10\_finseq\_1~\\
(k1\_funct\_1~k4\_twoscomp~(k10\_finseq\_1~X0~X1))~(k1\_funct\_1~k2\_twoscomp~\\
(k10\_finseq\_1~X0~X1)))){\unicdcdcdhd}((k1\_funct\_1~k4\_gfacirc1~(k10\_finseq\_1~\\
k6\_numbers~k6\_numbers)=np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k4\_gfacirc1~(k10\_finseq\_1~\\
k6\_numbers~np\_\_1)=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k4\_gfacirc1~(k10\_finseq\_1~\\
np\_\_1~k6\_numbers)=k6\_numbers){\unicdcdcdhd}(k1\_funct\_1~k4\_gfacirc1~(k10\_finseq\_1~\\
np\_\_1~np\_\_1)=np\_\_1))))))))\end{array}$$
\end{theorem}
\end{document}
