\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{t108\_aofa\_000 (TMYJEanM6YEtxQSBCcGtxwL6g6W93QB3tp4)}
\maketitle
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\_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 $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ m1\_aofa\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r7\_aofa\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\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 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~\\
X0){\unicdcdcdhd}((v3\_unialg\_1~X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}((v3\_aofa\_000~X0){\unicdcdcdhd}\\
((v4\_aofa\_000~X0){\unicdcdcdhd}((v5\_aofa\_000~X0){\unicdcdcdhd}((v6\_aofa\_000~X0){\unicdcdcdhd}(l1\_unialg\_1~\\
X0))))))))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_aofa\_000~X3~X0~X1~X2){\unicdbdjdcd}((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k2\_zfmisc\_1~X1~(u1\_struct\_0~X0))~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~(u1\_struct\_0~X0))~\\
X1))))))\end{array}
\label{hyp:egehpfngbdpfbgpgggbgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_unialg\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpffhogjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((\\
v1\_funct\_2~X3~(k2\_zfmisc\_1~X0~X1)~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~X2))))){\unicdcdcdhd}((m1\_subset\_1~X4~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X5~X1))))){\unicdbdjdcd}(m1\_subset\_1~(k2\_binop\_1~X0~X1~X2~X3~X4~\\
X5)~X2)\end{array}
\label{hyp:egehpflgcdpfcgjgogpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}((v3\_aofa\_000~X0){\unicdcdcdhd}((v4\_aofa\_000~X0){\unicdcdcdhd}\\
((v5\_aofa\_000~X0){\unicdcdcdhd}((v6\_aofa\_000~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_aofa\_000~X4~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X5 .  (r7\_aofa\_000~X0~X1~X2~X3~X4~\\
X5){\unicdbdjded}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X1){\unicdbdjdcd}((X6 \in X5){\unicdbdjdcd}(k2\_binop\_1~X1~\\
(u1\_struct\_0~X0)~X1~X4~X6~X3 \in X5))))))))\end{array}
\label{hyp:egddjdpfbgpgggbgpfadadad}
\end{equation}
\begin{theorem}\label{thm:ehbdadidpfbgpgggbgpfadadad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}((v3\_aofa\_000~X0){\unicdcdcdhd}((v4\_aofa\_000~X0){\unicdcdcdhd}\\
((v5\_aofa\_000~X0){\unicdcdcdhd}((v6\_aofa\_000~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_aofa\_000~X3~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(r7\_aofa\_000~X0~X1~X2~X4~X3~X1)))))\end{array}$$
\end{theorem}
\end{document}
