\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{t65\_facirc\_1 (TMH4UaN71E5VJ74gjBwnrgnqRvDwHXq99qs)}
\maketitle
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_facirc\_1 : {\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 $ k8\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k10\_facirc\_1 : {{\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 $ k11\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k9\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ 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}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~\\
k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(\\
k4\_card\_3~(u3\_msualg\_1~(k8\_facirc\_1~X1~X2~X0~X3)~(k10\_facirc\_1~\\
X1~X2~X0~X3)))){\unicdbdjdcd}((X0{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X1~X2)~X3){\unicdbdjdcd}((k11\_facirc\_1~\\
(k8\_facirc\_1~X1~X2~X0~X3)~(k10\_facirc\_1~X1~X2~X0~X3)~(k5\_facirc\_1~\\
(k8\_facirc\_1~X1~X2~X0~X3)~(k10\_facirc\_1~X1~X2~X0~X3)~X4~np\_\_2)~(k9\_facirc\_1~\\
X1~X2~X0~X3)=k1\_funct\_1~X3~(k10\_finseq\_1~(k1\_funct\_1~X3~(k10\_finseq\_1~\\
(k1\_funct\_1~X4~X1)~(k1\_funct\_1~X4~X2)))~(k1\_funct\_1~X4~X0))){\unicdcdcdhd}((\\
k1\_funct\_1~(k5\_facirc\_1~(k8\_facirc\_1~X1~X2~X0~X3)~(k10\_facirc\_1~\\
X1~X2~X0~X3)~X4~np\_\_2)~(k4\_tarski~(k10\_finseq\_1~X1~X2)~X3)=k1\_funct\_1~\\
X3~(k10\_finseq\_1~(k1\_funct\_1~X4~X1)~(k1\_funct\_1~X4~X2))){\unicdcdcdhd}((k1\_funct\_1~\\
(k5\_facirc\_1~(k8\_facirc\_1~X1~X2~X0~X3)~(k10\_facirc\_1~X1~X2~X0~X3)~\\
X4~np\_\_2)~X1=k1\_funct\_1~X4~X1){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(k8\_facirc\_1~\\
X1~X2~X0~X3)~(k10\_facirc\_1~X1~X2~X0~X3)~X4~np\_\_2)~X2=k1\_funct\_1~X4~X2){\unicdcdcdhd}\\
(k1\_funct\_1~(k5\_facirc\_1~(k8\_facirc\_1~X1~X2~X0~X3)~(k10\_facirc\_1~\\
X1~X2~X0~X3)~X4~np\_\_2)~X0=k1\_funct\_1~X4~X0)))))))\end{array}
\label{hyp:ehgdcdpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k2\_facirc\_1){\unicdcdcdhd}((v1\_funct\_2~k2\_facirc\_1~(k4\_finseq\_2~\\
np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k2\_facirc\_1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgcdpfggbgdgjgchdgpfbd}
\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}{\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=k2\_facirc\_1){\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)=k1\_binarith~\\
X1~X2))))\end{array}
\label{hyp:egfdpfggbgdgjgchdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdfdpfggbgdgjgchdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X0{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~k2\_facirc\_1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~(u3\_msualg\_1~\\
(k8\_facirc\_1~X1~X2~X0~k2\_facirc\_1)~(k10\_facirc\_1~X1~X2~X0~k2\_facirc\_1)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k6\_margrel1){\unicdbdjdcd}((\\
(X4=k1\_funct\_1~X3~X1){\unicdcdcdhd}((X5=k1\_funct\_1~X3~X2){\unicdcdcdhd}(X6=k1\_funct\_1~\\
X3~X0))){\unicdbdjdcd}(k11\_facirc\_1~(k8\_facirc\_1~X1~X2~X0~k2\_facirc\_1)~(k10\_facirc\_1~\\
X1~X2~X0~k2\_facirc\_1)~(k5\_facirc\_1~(k8\_facirc\_1~X1~X2~X0~k2\_facirc\_1)~\\
(k10\_facirc\_1~X1~X2~X0~k2\_facirc\_1)~X3~np\_\_2)~(k9\_facirc\_1~X1~X2~\\
X0~k2\_facirc\_1)=k1\_binarith~(k1\_binarith~X4~X5)~X6))))))\end{array}$$
\end{theorem}
\end{document}
