\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{t11\_msualg\_6 (TMQ8FQCtsJUZxg1xbHY8o5kZt8cjv51nQVs)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u3\_msualg\_1 : {{\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.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u4\_struct\_0~X0)){\unicdbdjdcd}((k3\_msualg\_1~X0~X2~X1=k4\_card\_3~(k3\_relat\_1~\\
(k1\_msualg\_1~X0~X2)~(u3\_msualg\_1~X0~X1))){\unicdcdcdhd}((k9\_xtuple\_0~(k3\_relat\_1~\\
(k1\_msualg\_1~X0~X2)~(u3\_msualg\_1~X0~X1))=k9\_xtuple\_0~(k1\_msualg\_1~\\
X0~X2)){\unicdcdcdhd}(k4\_msualg\_1~X0~X2~X1=k1\_funct\_1~(u3\_msualg\_1~X0~X1)~(k2\_msualg\_1~\\
X0~X2))))))\end{array}
\label{hyp:ehddpfahchbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l3\_msualg\_1~X2~X0){\unicdbdjdcd}((k3\_msualg\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdbdjded}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}(\preoh (X3 \in k4\_finseq\_1~(k1\_msualg\_1~\\
X0~X1)){\unicdcdcdhd}(k1\_funct\_1~(u3\_msualg\_1~X0~X2)~(k7\_partfun1~(u1\_struct\_0~\\
X0)~(k1\_msualg\_1~X0~X1)~X3)=k1\_xboole\_0))))))\end{array}
\label{hyp:ehddpfngdhfhbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_msualg\_6~X3~X0){\unicdcdcdhd}\\
(l3\_msualg\_1~X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~\\
X4)){\unicdbdjdcd}((X4 \in k3\_msualg\_1~X0~X1~X3){\unicdbdjdcd}((v1\_funct\_1~(k4\_msualg\_6~X0~\\
X1~X2~X3~X4)){\unicdcdcdhd}((v1\_funct\_2~(k4\_msualg\_6~X0~X1~X2~X3~X4)~(k1\_funct\_1~\\
(u3\_msualg\_1~X0~X3)~(k7\_partfun1~(u1\_struct\_0~X0)~(k1\_msualg\_1~\\
X0~X1)~X2))~(k1\_funct\_1~(u3\_msualg\_1~X0~X3)~(k2\_msualg\_1~X0~X1))){\unicdcdcdhd}\\
(m1\_subset\_1~(k4\_msualg\_6~X0~X1~X2~X3~X4)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_funct\_1~(u3\_msualg\_1~X0~X3)~(k7\_partfun1~(u1\_struct\_0~X0)~\\
(k1\_msualg\_1~X0~X1)~X2))~(k1\_funct\_1~(u3\_msualg\_1~X0~X3)~(k2\_msualg\_1~\\
X0~X1))))))))))))\end{array}
\label{hyp:ehbdadpfngdhfhbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (l3\_msualg\_1~X3~\\
X0){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}((r1\_msualg\_6~\\
X0~X1~X2~X3~X4){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u4\_struct\_0~X0)){\unicdcdcdhd}(\\
(k2\_msualg\_1~X0~X5=X2){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~k5\_numbers){\unicdcdcdhd}\\
((X6 \in k4\_finseq\_1~(k1\_msualg\_1~X0~X5)){\unicdcdcdhd}((k7\_partfun1~(u1\_struct\_0~\\
X0)~(k1\_msualg\_1~X0~X5)~X6=X1){\unicdcdcdhd}({\unicdcdaddd} X7 .  ((v1\_relat\_1~X7){\unicdcdcdhd}(\\
v1\_funct\_1~X7)){\unicdcdcdhd}((X7 \in k3\_msualg\_1~X0~X5~X3){\unicdcdcdhd}(X4=k4\_msualg\_6~X0~\\
X5~X6~X3~X7)))))))))))))\end{array}
\label{hyp:egfdpfngdhfhbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}((v1\_msualg\_6~X1~X0){\unicdbdjded}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~X0)){\unicdbdjdcd}(\preoh (k3\_msualg\_1~\\
X0~X2~X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k4\_msualg\_1~X0~X2~X1=k1\_xboole\_0)))))\end{array}
\label{hyp:egbdpfngdhfhbgmghgpfgd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfngdhfhbgmghgpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_msualg\_6~\\
X3~X0){\unicdcdcdhd}(l3\_msualg\_1~X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~\\
X4)){\unicdbdjdcd}((r1\_msualg\_6~X0~X1~X2~X3~X4){\unicdbdjdcd}(((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~(k1\_funct\_1~(u3\_msualg\_1~X0~X3)~X1)~(k1\_funct\_1~(u3\_msualg\_1~\\
X0~X3)~X2)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_funct\_1~\\
(u3\_msualg\_1~X0~X3)~X1)~(k1\_funct\_1~(u3\_msualg\_1~X0~X3)~X2)))))){\unicdcdcdhd}\\
((k1\_funct\_1~(u3\_msualg\_1~X0~X3)~X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k1\_funct\_1~\\
(u3\_msualg\_1~X0~X3)~X2{\unicdcdgdad}k1\_xboole\_0))))))))\end{array}$$
\end{theorem}
\end{document}
