\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{t94\_aofa\_000 (TMUPH2KLk4aaxbbnAKXBvX6RhHBwckzcDm6)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ 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\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_aofa\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k13\_aofa\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k14\_aofa\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k16\_aofa\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1 \in \\
k2\_zfmisc\_1~X2~X3){\unicdbdjded}((X0 \in X2){\unicdcdcdhd}(X1 \in X3))\end{array}
\label{hyp:ehidhdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\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)){\unicdcdcdhd}(m1\_aofa\_000~X3~X0~X1~X2)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k21\_aofa\_000~X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~(u1\_struct\_0~\\
X0))))\end{array}
\label{hyp:egehpflgcdbdpfbgpgggbgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\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\_aofa\_000~X3~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((X4=k21\_aofa\_000~\\
X0~X1~X2~X3){\unicdbdjded}((r1\_tarski~(k2\_zfmisc\_1~X1~(k18\_aofa\_000~X0))~X4){\unicdcdcdhd}\\
((r1\_tarski~(k2\_zfmisc\_1~X1~(k1\_tarski~(k12\_aofa\_000~X0)))~X4){\unicdcdcdhd}\\
(({\unicdcdadad} X5 .  (m1\_subset\_1~X5~X1){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}((((k4\_tarski~\\
X5~X7 \in X4){\unicdcdcdhd}(k4\_tarski~(k2\_binop\_1~X1~(u1\_struct\_0~X0)~X1~X3~X5~X7)~\\
X8 \in X4)){\unicdbdjdcd}(k4\_tarski~X5~(k13\_aofa\_000~X0~X7~X8) \in X4)){\unicdcdcdhd}((((k4\_tarski~\\
X5~X6 \in X4){\unicdcdcdhd}((k4\_tarski~(k2\_binop\_1~X1~(u1\_struct\_0~X0)~X1~X3~X5~X6)~\\
X7 \in X4){\unicdcdcdhd}(k2\_binop\_1~X1~(u1\_struct\_0~X0)~X1~X3~X5~X6 \in X2))){\unicdbdjdcd}(k4\_tarski~\\
X5~(k14\_aofa\_000~X0~X6~X7~X8) \in X4)){\unicdcdcdhd}((((k4\_tarski~X5~X6 \in X4){\unicdcdcdhd}(k4\_tarski~\\
(k2\_binop\_1~X1~(u1\_struct\_0~X0)~X1~X3~X5~X6)~X8 \in X4)){\unicdbdjdcd}((k2\_binop\_1~\\
X1~(u1\_struct\_0~X0)~X1~X3~X5~X6 \in X2){\unicdcdcdid}(k4\_tarski~X5~(k14\_aofa\_000~\\
X0~X6~X7~X8) \in X4))){\unicdcdcdhd}((k4\_tarski~X5~X6 \in X4){\unicdbdjdcd}(({\unicdcdadad} X9 .  ((\preoh v1\_xboole\_0~\\
X9){\unicdcdcdhd}(m2\_finseq\_1~X9~X1)){\unicdbdjdcd}(\preoh (k1\_funct\_1~X9~np\_\_1=k2\_binop\_1~X1~\\
(u1\_struct\_0~X0)~X1~X3~X5~X6){\unicdcdcdhd}((\preoh k1\_funct\_1~X9~(k3\_finseq\_1~X9) \in \\
X2){\unicdcdcdhd}({\unicdcdadad} X10 .  (v7\_ordinal1~X10){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X10){\unicdbdjdcd}\\
((r1\_xxreal\_0~(k3\_finseq\_1~X9)~X10){\unicdcdcdid}((k1\_funct\_1~X9~X10 \in X2){\unicdcdcdhd}\\
((k4\_tarski~(k1\_funct\_1~X9~X10)~(k13\_aofa\_000~X0~X7~X6) \in X4){\unicdcdcdhd}(k1\_funct\_1~\\
X9~(k1\_nat\_1~X10~np\_\_1)=k1\_binop\_1~X3~(k1\_funct\_1~X9~X10)~(k13\_aofa\_000~\\
X0~X7~X6)))))))))){\unicdcdcdid}(k4\_tarski~X5~(k16\_aofa\_000~X0~X6~X7) \in X4)))))))))){\unicdcdcdhd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(((r1\_tarski~(k2\_zfmisc\_1~X1~(k18\_aofa\_000~X0))~X5){\unicdcdcdhd}(\\
(r1\_tarski~(k2\_zfmisc\_1~X1~(k1\_tarski~(k12\_aofa\_000~X0)))~X5){\unicdcdcdhd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X1){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(\\
u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~X0)){\unicdbdjdcd}((((k4\_tarski~\\
X6~X8 \in X5){\unicdcdcdhd}(k4\_tarski~(k2\_binop\_1~X1~(u1\_struct\_0~X0)~X1~X3~X6~X8)~\\
X9 \in X5)){\unicdbdjdcd}(k4\_tarski~X6~(k13\_aofa\_000~X0~X8~X9) \in X5)){\unicdcdcdhd}((((k4\_tarski~\\
X6~X7 \in X5){\unicdcdcdhd}((k4\_tarski~(k2\_binop\_1~X1~(u1\_struct\_0~X0)~X1~X3~X6~X7)~\\
X8 \in X5){\unicdcdcdhd}(k2\_binop\_1~X1~(u1\_struct\_0~X0)~X1~X3~X6~X7 \in X2))){\unicdbdjdcd}(k4\_tarski~\\
X6~(k14\_aofa\_000~X0~X7~X8~X9) \in X5)){\unicdcdcdhd}((((k4\_tarski~X6~X7 \in X5){\unicdcdcdhd}(k4\_tarski~\\
(k2\_binop\_1~X1~(u1\_struct\_0~X0)~X1~X3~X6~X7)~X9 \in X5)){\unicdbdjdcd}((k2\_binop\_1~\\
X1~(u1\_struct\_0~X0)~X1~X3~X6~X7 \in X2){\unicdcdcdid}(k4\_tarski~X6~(k14\_aofa\_000~\\
X0~X7~X8~X9) \in X5))){\unicdcdcdhd}((k4\_tarski~X6~X7 \in X5){\unicdbdjdcd}(({\unicdcdadad} X10 .  ((\preoh v1\_xboole\_0~\\
X10){\unicdcdcdhd}(m2\_finseq\_1~X10~X1)){\unicdbdjdcd}(\preoh (k1\_funct\_1~X10~np\_\_1=k2\_binop\_1~\\
X1~(u1\_struct\_0~X0)~X1~X3~X6~X7){\unicdcdcdhd}((\preoh k1\_funct\_1~X10~(k3\_finseq\_1~\\
X10) \in X2){\unicdcdcdhd}({\unicdcdadad} X11 .  (v7\_ordinal1~X11){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~\\
X11){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X10)~X11){\unicdcdcdid}((k1\_funct\_1~X10~X11 \in \\
X2){\unicdcdcdhd}((k4\_tarski~(k1\_funct\_1~X10~X11)~(k13\_aofa\_000~X0~X8~X7) \in X5){\unicdcdcdhd}\\
(k1\_funct\_1~X10~(k1\_nat\_1~X11~np\_\_1)=k1\_binop\_1~X3~(k1\_funct\_1~\\
X10~X11)~(k13\_aofa\_000~X0~X8~X7)))))))))){\unicdcdcdid}(k4\_tarski~X6~(k16\_aofa\_000~\\
X0~X7~X8) \in X5)))))))))))){\unicdbdjdcd}(r1\_relset\_1~X1~(u1\_struct\_0~X0)~X4~X5)))))))))))\end{array}
\label{hyp:egddfdpfbgpgggbgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((m1\_subset\_1~X1~X0){\unicdbdjded}\\
(X1 \in X0))){\unicdcdcdhd}((v1\_xboole\_0~X0){\unicdbdjdcd}((m1\_subset\_1~X1~X0){\unicdbdjded}(v1\_xboole\_0~\\
X1)))\end{array}
\label{hyp:egbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehjdedpfbgpgggbgpfadadad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}((v3\_aofa\_000~X0){\unicdcdcdhd}((v4\_aofa\_000~X0){\unicdcdcdhd}\\
((v5\_aofa\_000~X0){\unicdcdcdhd}((v6\_aofa\_000~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh \\
v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~X2)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X2){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_aofa\_000~X5~X0~\\
X2~X3){\unicdbdjdcd}((X1 \in k18\_aofa\_000~X0){\unicdbdjdcd}(k4\_tarski~X4~X1 \in k21\_aofa\_000~X0~\\
X2~X3~X5)))))))\end{array}$$
\end{theorem}
\end{document}
