\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{t103\_aofa\_000 (TMb23ao6r1YWhYMeT2wrbhnTP7g95nGnLMY)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_freealg : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_aofa\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_aofa\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_aofa\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_aofa\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_aofa\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_aofa\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k18\_aofa\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k21\_aofa\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_unialg\_1~X2){\unicdcdcdhd}((v3\_unialg\_1~\\
X2){\unicdcdcdhd}((v4\_unialg\_1~X2){\unicdcdcdhd}((v3\_freealg~X2){\unicdcdcdhd}((v3\_aofa\_000~X2){\unicdcdcdhd}(\\
(v4\_aofa\_000~X2){\unicdcdcdhd}((v5\_aofa\_000~X2){\unicdcdcdhd}((v6\_aofa\_000~X2){\unicdcdcdhd}((v12\_aofa\_000~\\
X2){\unicdcdcdhd}(l1\_unialg\_1~X2))))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_aofa\_000~X3~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_aofa\_000~X4~X2~X0~X1){\unicdbdjdcd}((r2\_relset\_1~(\\
k2\_zfmisc\_1~X0~(u1\_struct\_0~X2))~X0~(k2\_partfun1~(k2\_zfmisc\_1~\\
X0~(u1\_struct\_0~X2))~X0~X3~(k2\_zfmisc\_1~X0~(k18\_aofa\_000~X2)))~(\\
k2\_partfun1~(k2\_zfmisc\_1~X0~(u1\_struct\_0~X2))~X0~X4~(k2\_zfmisc\_1~\\
X0~(k18\_aofa\_000~X2)))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X0){\unicdbdjdcd}((k4\_tarski~X6~X5 \in k21\_aofa\_000~\\
X2~X0~X1~X3){\unicdbdjdcd}((k4\_tarski~X6~X5 \in k21\_aofa\_000~X2~X0~X1~X4){\unicdcdcdhd}(k2\_binop\_1~\\
X0~(u1\_struct\_0~X2)~X0~X3~X6~X5=k2\_binop\_1~X0~(u1\_struct\_0~X2)~X0~\\
X4~X6~X5))))))))))\end{array}
\label{hyp:mgbdedddpfbgpgggbgpfadadad}
\end{equation}
\begin{theorem}\label{thm:ehbdadddpfbgpgggbgpfadadad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_unialg\_1~X2){\unicdcdcdhd}((v3\_unialg\_1~\\
X2){\unicdcdcdhd}((v4\_unialg\_1~X2){\unicdcdcdhd}((v3\_freealg~X2){\unicdcdcdhd}((v3\_aofa\_000~X2){\unicdcdcdhd}(\\
(v4\_aofa\_000~X2){\unicdcdcdhd}((v5\_aofa\_000~X2){\unicdcdcdhd}((v6\_aofa\_000~X2){\unicdcdcdhd}((v12\_aofa\_000~\\
X2){\unicdcdcdhd}(l1\_unialg\_1~X2))))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_aofa\_000~X3~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_aofa\_000~X4~X2~X0~X1){\unicdbdjdcd}((r2\_relset\_1~(\\
k2\_zfmisc\_1~X0~(u1\_struct\_0~X2))~X0~(k2\_partfun1~(k2\_zfmisc\_1~\\
X0~(u1\_struct\_0~X2))~X0~X3~(k2\_zfmisc\_1~X0~(k18\_aofa\_000~X2)))~(\\
k2\_partfun1~(k2\_zfmisc\_1~X0~(u1\_struct\_0~X2))~X0~X4~(k2\_zfmisc\_1~\\
X0~(k18\_aofa\_000~X2)))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~X0){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X2)){\unicdbdjdcd}((k4\_tarski~X5~X6 \in k21\_aofa\_000~\\
X2~X0~X1~X3){\unicdbdjdcd}(k2\_binop\_1~X0~(u1\_struct\_0~X2)~X0~X3~X5~X6=k2\_binop\_1~\\
X0~(u1\_struct\_0~X2)~X0~X4~X5~X6)))))))))\end{array}$$
\end{theorem}
\end{document}
