\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\_3 (TMGABFK2xp9CAzkiNS7JCyUZHVKowPDhDzC)}
\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 $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\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 $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_msualg\_1 : {{\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}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_pboole~X4~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k3\_msualg\_1~X0~X3~X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
((v1\_relat\_1~X6){\unicdcdcdhd}(v1\_funct\_1~X6)){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_relat\_1~\\
X7){\unicdcdcdhd}(v1\_funct\_1~X7)){\unicdbdjdcd}(((X5=X6){\unicdcdcdhd}((X5 \in k3\_msualg\_1~X0~X3~X1){\unicdcdcdhd}(\\
X7 \in k3\_msualg\_1~X0~X3~X2))){\unicdbdjdcd}(((X7=k5\_msualg\_3~X0~X1~X2~X3~X4~X5){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (v7\_ordinal1~X8){\unicdbdjdcd}((X8 \in k9\_xtuple\_0~X6){\unicdbdjdcd}(k1\_funct\_1~\\
X7~X8=k1\_funct\_1~(k1\_msualg\_3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~\\
X1)~(u3\_msualg\_1~X0~X2)~X4~(k7\_partfun1~(u1\_struct\_0~X0)~(k1\_msualg\_1~\\
X0~X3)~X8))~(k1\_funct\_1~X6~X8))))){\unicdcdcdhd}(({\unicdcdadad} X8 .  (v7\_ordinal1~X8){\unicdbdjdcd}\\
((X8 \in k9\_xtuple\_0~X6){\unicdbdjdcd}(k1\_funct\_1~X7~X8=k1\_funct\_1~(k1\_msualg\_3~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X2)~X4~(k7\_partfun1~\\
(u1\_struct\_0~X0)~(k1\_msualg\_1~X0~X3)~X8))~(k1\_funct\_1~X6~X8)))){\unicdbdjdcd}\\
(X7=k5\_msualg\_3~X0~X1~X2~X3~X4~X5)))))))))))\end{array}
\label{hyp:mgbdcdpfngdhfhbgmghgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfngdhfhbgmghgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_pboole~X4~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k3\_msualg\_1~X0~X3~X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
((v1\_relat\_1~X6){\unicdcdcdhd}(v1\_funct\_1~X6)){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_relat\_1~\\
X7){\unicdcdcdhd}(v1\_funct\_1~X7)){\unicdbdjdcd}(((X5=X6){\unicdcdcdhd}((X5 \in k3\_msualg\_1~X0~X3~X1){\unicdcdcdhd}(\\
X7 \in k3\_msualg\_1~X0~X3~X2))){\unicdbdjdcd}((X7=k5\_msualg\_3~X0~X1~X2~X3~X4~X5){\unicdbdjded}(\\
{\unicdcdadad} X8 .  (v7\_ordinal1~X8){\unicdbdjdcd}((X8 \in k9\_xtuple\_0~X6){\unicdbdjdcd}(k1\_funct\_1~\\
X7~X8=k1\_funct\_1~(k1\_msualg\_3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~\\
X1)~(u3\_msualg\_1~X0~X2)~X4~(k7\_partfun1~(u1\_struct\_0~X0)~(k1\_msualg\_1~\\
X0~X3)~X8))~(k1\_funct\_1~X6~X8)))))))))))))\end{array}$$
\end{theorem}
\end{document}
