\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{t24\_msualg\_6 (TMT5866ciUpL6WmmCS31v3fbLzQp1Ged2U4)}
\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 $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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\_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\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ 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}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v4\_msualg\_1~X2~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_pboole~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X2)){\unicdbdjdcd}((r1\_msualg\_3~X0~X1~X2~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}(v1\_funct\_1~X6)){\unicdbdjdcd}(\preoh (r1\_msualg\_6~\\
X0~X4~X5~X1~X6){\unicdcdcdhd}({\unicdcdadad} X7 .  ((v1\_funct\_1~X7){\unicdcdcdhd}((v1\_funct\_2~X7~(k1\_funct\_1~\\
(u3\_msualg\_1~X0~X2)~X4)~(k1\_funct\_1~(u3\_msualg\_1~X0~X2)~X5)){\unicdcdcdhd}(m1\_subset\_1~\\
X7~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_funct\_1~(u3\_msualg\_1~X0~X2)~X4)~\\
(k1\_funct\_1~(u3\_msualg\_1~X0~X2)~X5)))))){\unicdbdjdcd}(\preoh (r1\_msualg\_6~X0~X4~\\
X5~X2~X7){\unicdcdcdhd}(k1\_partfun1~(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~X4)~(k1\_funct\_1~\\
(u3\_msualg\_1~X0~X2)~X4)~(k1\_funct\_1~(u3\_msualg\_1~X0~X2)~X4)~(k1\_funct\_1~\\
(u3\_msualg\_1~X0~X2)~X5)~(k1\_msualg\_3~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~(u3\_msualg\_1~X0~X2)~X3~X4)~X7=k3\_relat\_1~X6~(k1\_msualg\_3~(\\
u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X2)~X3~X5))))))))))))\end{array}
\label{hyp:ehcdddpfngdhfhbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_msualg\_6~\\
X2~X0~X1){\unicdbdjdcd}(m2\_pboole~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X1)))\end{array}
\label{hyp:egehpfngbdpfngdhfhbgmghgpfgd}
\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 .  (m2\_pboole~\\
X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)){\unicdbdjdcd}((\\
m1\_msualg\_6~X2~X0~X1){\unicdbdjded}(r1\_msualg\_3~X0~X1~X1~X2))))\end{array}
\label{hyp:egcdpfngdhfhbgmghgpfgd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfngdhfhbgmghgpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_msualg\_6~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}(v1\_funct\_1~X5)){\unicdbdjdcd}(\preoh (r1\_msualg\_6~\\
X0~X3~X4~X1~X5){\unicdcdcdhd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~(k1\_funct\_1~\\
(u3\_msualg\_1~X0~X1)~X3)~(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~X4)){\unicdcdcdhd}(m1\_subset\_1~\\
X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~X3)~\\
(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~X4)))))){\unicdbdjdcd}(\preoh (r1\_msualg\_6~X0~X3~\\
X4~X1~X6){\unicdcdcdhd}(k1\_partfun1~(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~X3)~(k1\_funct\_1~\\
(u3\_msualg\_1~X0~X1)~X3)~(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~X3)~(k1\_funct\_1~\\
(u3\_msualg\_1~X0~X1)~X4)~(k1\_msualg\_3~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~(u3\_msualg\_1~X0~X1)~X2~X3)~X6=k3\_relat\_1~X5~(k1\_msualg\_3~(\\
u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)~X2~X4))))))))))\end{array}$$
\end{theorem}
\end{document}
