\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{t51\_facirc\_1 (TMbq11jZu3vLLn9Uo1bqkzdTTdDk5CCsp86)}
\maketitle
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 $ k6\_margrel1 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_circuit2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_circuit2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(v1\_finset\_1~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k4\_finseq\_2~\\
np\_\_2~X2)~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~\\
np\_\_2~X2)~X2))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k4\_card\_3~(u3\_msualg\_1~\\
(k5\_circcomb~X3~(k10\_finseq\_1~X0~X1))~(k7\_circcomb~np\_\_2~X2~X3~(\\
k10\_finseq\_1~X0~X1))))){\unicdbdjdcd}(v1\_circuit2~(k6\_circuit2~(k5\_circcomb~\\
X3~(k10\_finseq\_1~X0~X1))~(k7\_circcomb~np\_\_2~X2~X3~(k10\_finseq\_1~\\
X0~X1))~X4)~(k5\_circcomb~X3~(k10\_finseq\_1~X0~X1))~(k7\_circcomb~np\_\_2~\\
X2~X3~(k10\_finseq\_1~X0~X1)))))\end{array}
\label{hyp:ehedjdpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k6\_margrel1}}}}\label{hyp:ggdgcdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_finset\_1}~{({{{k2\_tarski}~{X0}}~{X1}})}}}}\label{hyp:ggdgcdpfggjgogdhfgehpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~\\
k6\_margrel1))))){\unicdbdjdcd}(k6\_facirc\_1~X0~X1~X2=k7\_circcomb~np\_\_2~k6\_margrel1~\\
X2~(k10\_finseq\_1~X0~X1))\end{array}
\label{hyp:egbdadpfggbgdgjgchdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdbdpfggbgdgjgchdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~\\
k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~(u3\_msualg\_1~\\
(k5\_circcomb~X2~(k10\_finseq\_1~X0~X1))~(k6\_facirc\_1~X0~X1~X2)))){\unicdbdjdcd}\\
(v1\_circuit2~(k6\_circuit2~(k5\_circcomb~X2~(k10\_finseq\_1~X0~X1))~\\
(k6\_facirc\_1~X0~X1~X2)~X3)~(k5\_circcomb~X2~(k10\_finseq\_1~X0~X1))~\\
(k6\_facirc\_1~X0~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
