\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{t83\_facirc\_1 (TMS2EzV84b7p3E5vJNt3HWtSTL9CHjnJmPf)}
\maketitle
Let $ v1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k15\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k18\_facirc\_1 : {{\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 $ k17\_facirc\_1 : {{\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 $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_facirc\_1 : {\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 .  (m1\_subset\_1~X3~(k4\_card\_3~\\
(u3\_msualg\_1~(k15\_facirc\_1~X0~X1~X2)~(k18\_facirc\_1~X0~X1~X2)))){\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~X0){\unicdcdcdhd}((X5=k1\_funct\_1~X3~X1){\unicdcdcdhd}(X6=k1\_funct\_1~\\
X3~X2))){\unicdbdjdcd}((k11\_facirc\_1~(k15\_facirc\_1~X0~X1~X2)~(k18\_facirc\_1~\\
X0~X1~X2)~(k5\_facirc\_1~(k15\_facirc\_1~X0~X1~X2)~(k18\_facirc\_1~X0~X1~\\
X2)~X3~np\_\_2)~(k17\_facirc\_1~X0~X1~X2)=k1\_binarith~(k1\_binarith~\\
(k10\_margrel1~X4~X5)~(k10\_margrel1~X5~X6))~(k10\_margrel1~X6~X4)){\unicdcdcdhd}\\
((k1\_funct\_1~(k5\_facirc\_1~(k15\_facirc\_1~X0~X1~X2)~(k18\_facirc\_1~\\
X0~X1~X2)~X3~np\_\_2)~(k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_facirc\_1)=\\
k10\_margrel1~X4~X5){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(k15\_facirc\_1~\\
X0~X1~X2)~(k18\_facirc\_1~X0~X1~X2)~X3~np\_\_2)~(k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~k3\_facirc\_1)=k10\_margrel1~X5~X6){\unicdcdcdhd}(k1\_funct\_1~(k5\_facirc\_1~\\
(k15\_facirc\_1~X0~X1~X2)~(k18\_facirc\_1~X0~X1~X2)~X3~np\_\_2)~(k4\_tarski~\\
(k10\_finseq\_1~X2~X0)~k3\_facirc\_1)=k10\_margrel1~X6~X4)))))))))))\end{array}
\label{hyp:mgbdadddpfggbgdgjgchdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehidddpfggbgdgjgchdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xtuple\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~\\
(u3\_msualg\_1~(k15\_facirc\_1~X0~X1~X2)~(k18\_facirc\_1~X0~X1~X2)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k6\_margrel1){\unicdbdjdcd}((\\
(X4=k1\_funct\_1~X3~X0){\unicdcdcdhd}((X5=k1\_funct\_1~X3~X1){\unicdcdcdhd}(X6=k1\_funct\_1~\\
X3~X2))){\unicdbdjdcd}(k11\_facirc\_1~(k15\_facirc\_1~X0~X1~X2)~(k18\_facirc\_1~X0~\\
X1~X2)~(k5\_facirc\_1~(k15\_facirc\_1~X0~X1~X2)~(k18\_facirc\_1~X0~X1~X2)~\\
X3~np\_\_2)~(k17\_facirc\_1~X0~X1~X2)=k1\_binarith~(k1\_binarith~(k10\_margrel1~\\
X4~X5)~(k10\_margrel1~X5~X6))~(k10\_margrel1~X6~X4)))))))))\end{array}$$
\end{theorem}
\end{document}
