\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{t12\_msualg\_6 (TMT6C3GuBFfTRgDRfxVgLNihfjHf2b97WqY)}
\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 $ 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 $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_msualg\_6 : {{\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 $ u4\_struct\_0 : {{\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 $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_msualg\_1 : {{\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}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k3\_msualg\_6~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgddpfngdhfhbgmghgpfgd}
\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 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))){\unicdbdjdcd}((X1=k3\_msualg\_6~X0){\unicdbdjded}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((k4\_tarski~X2~X3 \in X1){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~(u4\_struct\_0~X0)){\unicdcdcdhd}((k2\_msualg\_1~X0~X4=X3){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~\\
X5~k5\_numbers){\unicdcdcdhd}((X5 \in k4\_finseq\_1~(k1\_msualg\_1~X0~X4)){\unicdcdcdhd}(k7\_partfun1~\\
(u1\_struct\_0~X0)~(k1\_msualg\_1~X0~X4)~X5=X2))))))))))\end{array}
\label{hyp:egddpfngdhfhbgmghgpfgd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfngdhfhbgmghgpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (l3\_msualg\_1~X3~\\
X0){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}((r1\_msualg\_6~\\
X0~X1~X2~X3~X4){\unicdbdjdcd}(k4\_tarski~X1~X2 \in k3\_msualg\_6~X0))))))\end{array}$$
\end{theorem}
\end{document}
