\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{t16\_fscirc\_1 (TMZcKdRsFAB6ipWKzTfkQBsMoLXNyaXdu3i)}
\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 $ k4\_fscirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_fscirc\_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 $ k5\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_2 : {\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\_twoscomp : {\iota}$ be given.
Let $ k10\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_fscirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_twoscomp : {\iota}$ be given.
Let $ v3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X0 \in u1\_struct\_0~(k4\_fscirc\_1~\\
X0~X1~X2)){\unicdcdcdhd}((X1 \in u1\_struct\_0~(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}(X2 \in u1\_struct\_0~\\
(k4\_fscirc\_1~X0~X1~X2)))\end{array}
\label{hyp:ehgdpfggdhdgjgchdgpfbd}
\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 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdcdcdhd}\\
(((v4\_msafree2~X1~X0){\unicdcdcdhd}((v6\_circcomb~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(k4\_card\_3~(u3\_msualg\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(u1\_struct\_0~X0))))){\unicdbdjdcd}(k11\_facirc\_1~X0~X1~X2~X3=k1\_funct\_1~X2~\\
X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfggbgdgjgchdgpfbd}
\end{equation}
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~(k4\_fscirc\_1~X0~X1~X2)~(k7\_fscirc\_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~(k4\_fscirc\_1~X0~X1~X2)~(k7\_fscirc\_1~X0~\\
X1~X2)~(k5\_facirc\_1~(k4\_fscirc\_1~X0~X1~X2)~(k7\_fscirc\_1~X0~X1~X2)~\\
X3~np\_\_2)~(k6\_fscirc\_1~X0~X1~X2)=k1\_binarith~(k1\_binarith~(k10\_margrel1~\\
(k9\_margrel1~X4)~X5)~(k10\_margrel1~X5~X6))~(k10\_margrel1~(k9\_margrel1~\\
X4)~X6)){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(k4\_fscirc\_1~X0~X1~X2)~(k7\_fscirc\_1~\\
X0~X1~X2)~X3~np\_\_2)~(k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_twoscomp)=\\
k10\_margrel1~(k9\_margrel1~X4)~X5){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~\\
(k4\_fscirc\_1~X0~X1~X2)~(k7\_fscirc\_1~X0~X1~X2)~X3~np\_\_2)~(k4\_tarski~\\
(k10\_finseq\_1~X1~X2)~k2\_twoscomp)=k10\_margrel1~X5~X6){\unicdcdcdhd}(k1\_funct\_1~\\
(k5\_facirc\_1~(k4\_fscirc\_1~X0~X1~X2)~(k7\_fscirc\_1~X0~X1~X2)~X3~np\_\_2)~\\
(k4\_tarski~(k10\_finseq\_1~X0~X2)~k3\_twoscomp)=k10\_margrel1~(k9\_margrel1~\\
X4)~X6)))))))))))\end{array}
\label{hyp:mgcdcdpfggdhdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v3\_msualg\_1~(k7\_fscirc\_1~X0~\\
X1~X2)~(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v4\_msafree2~(k7\_fscirc\_1~X0~X1~\\
X2)~(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v4\_circcomb~(k7\_fscirc\_1~X0~X1~X2)~\\
(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v6\_circcomb~(k7\_fscirc\_1~X0~X1~X2)~(k4\_fscirc\_1~\\
X0~X1~X2)){\unicdcdcdhd}(l3\_msualg\_1~(k7\_fscirc\_1~X0~X1~X2)~(k4\_fscirc\_1~X0~X1~\\
X2)))))\end{array}
\label{hyp:egehpflghdpfggdhdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v2\_struct\_0~(k4\_fscirc\_1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_circcomb~(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}\\
((v2\_circcomb~(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v3\_circcomb~(k4\_fscirc\_1~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_msualg\_1~(k4\_fscirc\_1~X0~X1~X2)))))))\end{array}
\label{hyp:egehpflgedpfggdhdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdcdcdhd}\\
(((v4\_msafree2~X1~X0){\unicdcdcdhd}((v6\_circcomb~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(k4\_card\_3~(u3\_msualg\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(u1\_struct\_0~X0))))){\unicdbdjdcd}(m1\_subset\_1~(k11\_facirc\_1~X0~X1~X2~X3)~\\
k6\_margrel1)\end{array}
\label{hyp:egehpflgbdbdpfggbgdgjgchdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfggdhdgjgchdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xtuple\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~\\
(u3\_msualg\_1~(k4\_fscirc\_1~X0~X1~X2)~(k7\_fscirc\_1~X0~X1~X2)))){\unicdbdjdcd}(\\
{\unicdcdadad} X4 .  (m1\_subset\_1~X4~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k6\_margrel1){\unicdbdjdcd}(((X4=k1\_funct\_1~X3~X0){\unicdcdcdhd}(X5=k1\_funct\_1~X3~X2)){\unicdbdjdcd}\\
(k1\_funct\_1~(k5\_facirc\_1~(k4\_fscirc\_1~X0~X1~X2)~(k7\_fscirc\_1~X0~\\
X1~X2)~X3~np\_\_2)~(k4\_tarski~(k10\_finseq\_1~X0~X2)~k3\_twoscomp)=k10\_margrel1~\\
(k9\_margrel1~X4)~X5)))))))\end{array}$$
\end{theorem}
\end{document}
