\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{t43\_aofa\_i00 (TMPPp97JvD6W52xowkJQP6ewp63iBSAWCNr)}
\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 $ v2\_aofa\_i00 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_card\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_aofa\_i00 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m1\_aofa\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m1\_aofa\_i00 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m3\_aofa\_i00 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k21\_aofa\_i00 : {{\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.
Let $ k55\_aofa\_i00 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k6\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k47\_aofa\_i00 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k42\_aofa\_i00 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k36\_aofa\_i00 : {{\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 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}((v2\_aofa\_i00~X0){\unicdcdcdhd}(l1\_unialg\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_card\_3~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_funct\_2~X2~X1~k4\_numbers~(k9\_funct\_2~X1~k4\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(k9\_funct\_2~X1~k4\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_aofa\_i00~X4~X0~X1~X3){\unicdcdcdhd}(m1\_aofa\_000~X4~X0~(k9\_funct\_2~\\
X1~k4\_numbers)~X3)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_aofa\_i00~X5~X1~(u1\_struct\_0~\\
X0)~(k9\_funct\_2~X1~k4\_numbers)~X4){\unicdbdjdcd}({\unicdcdadad} X6 .  (m3\_aofa\_i00~X6~\\
X0~X1~X3~X4){\unicdbdjdcd}((k21\_aofa\_i00~X1~k4\_numbers~(k2\_binop\_1~(k9\_funct\_2~\\
X1~k4\_numbers)~(u1\_struct\_0~X0)~(k9\_funct\_2~X1~k4\_numbers)~X4~X2~\\
(k47\_aofa\_i00~X0~X1~X3~X4~X5~X6))~X5=k3\_funct\_2~(k9\_funct\_2~X1~k4\_numbers)~\\
k4\_numbers~X6~X2){\unicdcdcdhd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~X1){\unicdbdjdcd}((X7{\unicdcdgdad}X5){\unicdbdjdcd}(\\
k21\_aofa\_i00~X1~k4\_numbers~(k2\_binop\_1~(k9\_funct\_2~X1~k4\_numbers)~\\
(u1\_struct\_0~X0)~(k9\_funct\_2~X1~k4\_numbers)~X4~X2~(k47\_aofa\_i00~\\
X0~X1~X3~X4~X5~X6))~X7=k21\_aofa\_i00~X1~k4\_numbers~X2~X7))))))))))\end{array}
\label{hyp:ehcdgdpfbgpgggbgpfjgadad}
\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}((v2\_aofa\_i00~X0){\unicdcdcdhd}(l1\_unialg\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_card\_3~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k9\_funct\_2~X1~k4\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_aofa\_i00~X3~X0~X1~X2){\unicdcdcdhd}(m1\_aofa\_000~X3~X0~(k9\_funct\_2~\\
X1~k4\_numbers)~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_aofa\_i00~X4~X1~(u1\_struct\_0~\\
X0)~(k9\_funct\_2~X1~k4\_numbers)~X3){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_funct\_2~X5~\\
X1~k4\_numbers~(k9\_funct\_2~X1~k4\_numbers)){\unicdbdjdcd}(k3\_funct\_2~(k9\_funct\_2~\\
X1~k4\_numbers)~k4\_numbers~(k42\_aofa\_i00~X0~X1~X2~X3~X4)~X5=k21\_aofa\_i00~\\
X1~k4\_numbers~X5~X4))))))\end{array}
\label{hyp:ehcdcdpfbgpgggbgpfjgadad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\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}((v2\_aofa\_i00~X0){\unicdcdcdhd}(l1\_unialg\_1~X0)))))))))){\unicdcdcdhd}(((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(v4\_card\_3~X1)){\unicdcdcdhd}((m1\_subset\_1~X2~(k1\_zfmisc\_1~(k9\_funct\_2~\\
X1~k4\_numbers))){\unicdcdcdhd}(((v1\_aofa\_i00~X3~X0~X1~X2){\unicdcdcdhd}(m1\_aofa\_000~X3~X0~\\
(k9\_funct\_2~X1~k4\_numbers)~X2)){\unicdcdcdhd}(m1\_aofa\_i00~X4~X1~(u1\_struct\_0~\\
X0)~(k9\_funct\_2~X1~k4\_numbers)~X3))))){\unicdbdjdcd}(m3\_aofa\_i00~(k42\_aofa\_i00~\\
X0~X1~X2~X3~X4)~X0~X1~X2~X3)\end{array}
\label{hyp:egehpflgedcdpfbgpgggbgpfjgadad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((\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}((v2\_aofa\_i00~X0){\unicdcdcdhd}(l1\_unialg\_1~X0)))))))))){\unicdcdcdhd}\\
(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_card\_3~X1)){\unicdcdcdhd}((m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k9\_funct\_2~X1~k4\_numbers))){\unicdcdcdhd}(((v1\_aofa\_i00~X3~X0~X1~X2){\unicdcdcdhd}(m1\_aofa\_000~\\
X3~X0~(k9\_funct\_2~X1~k4\_numbers)~X2)){\unicdcdcdhd}((m3\_aofa\_i00~X4~X0~X1~X2~X3){\unicdcdcdhd}\\
(m3\_aofa\_i00~X5~X0~X1~X2~X3)))))){\unicdbdjdcd}(m3\_aofa\_i00~(k36\_aofa\_i00~X0~\\
X1~X2~X3~X4~X5)~X0~X1~X2~X3)\end{array}
\label{hyp:egehpflgddgdpfbgpgggbgpfjgadad}
\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}((v2\_aofa\_i00~X0){\unicdcdcdhd}(l1\_unialg\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_card\_3~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k9\_funct\_2~X1~k4\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_aofa\_i00~X3~X0~X1~X2){\unicdcdcdhd}(m1\_aofa\_000~X3~X0~(k9\_funct\_2~\\
X1~k4\_numbers)~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_aofa\_i00~X4~X1~(u1\_struct\_0~\\
X0)~(k9\_funct\_2~X1~k4\_numbers)~X3){\unicdbdjdcd}({\unicdcdadad} X5 .  (m3\_aofa\_i00~X5~\\
X0~X1~X2~X3){\unicdbdjdcd}(k55\_aofa\_i00~X0~X1~X2~X3~X4~X5=k47\_aofa\_i00~X0~X1~X2~X3~\\
X4~(k36\_aofa\_i00~X0~X1~X2~X3~(k42\_aofa\_i00~X0~X1~X2~X3~X4)~X5)))))))\end{array}
\label{hyp:egedjdpfbgpgggbgpfjgadad}
\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}((v2\_aofa\_i00~X0){\unicdcdcdhd}(l1\_unialg\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_card\_3~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k9\_funct\_2~X1~k4\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_aofa\_i00~X3~X0~X1~X2){\unicdcdcdhd}(m1\_aofa\_000~X3~X0~(k9\_funct\_2~\\
X1~k4\_numbers)~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m3\_aofa\_i00~X4~X0~X1~X2~X3){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m3\_aofa\_i00~X5~X0~X1~X2~X3){\unicdbdjdcd}({\unicdcdadad} X6 .  (m3\_aofa\_i00~X6~X0~X1~X2~\\
X3){\unicdbdjdcd}((X6=k36\_aofa\_i00~X0~X1~X2~X3~X4~X5){\unicdbdjded}({\unicdcdadad} X7 .  (m2\_funct\_2~\\
X7~X1~k4\_numbers~(k9\_funct\_2~X1~k4\_numbers)){\unicdbdjdcd}(k3\_funct\_2~(k9\_funct\_2~\\
X1~k4\_numbers)~k4\_numbers~X6~X7=k6\_int\_1~(k3\_funct\_2~(k9\_funct\_2~\\
X1~k4\_numbers)~k4\_numbers~X4~X7)~(k3\_funct\_2~(k9\_funct\_2~X1~k4\_numbers)~\\
k4\_numbers~X5~X7))))))))))\end{array}
\label{hyp:egddadpfbgpgggbgpfjgadad}
\end{equation}
\begin{theorem}\label{thm:ehedddpfbgpgggbgpfjgadad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}((v3\_aofa\_000~X0){\unicdcdcdhd}((v4\_aofa\_000~X0){\unicdcdcdhd}\\
((v5\_aofa\_000~X0){\unicdcdcdhd}((v6\_aofa\_000~X0){\unicdcdcdhd}((v2\_aofa\_i00~X0){\unicdcdcdhd}(l1\_unialg\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_card\_3~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_funct\_2~X2~X1~k4\_numbers~(k9\_funct\_2~X1~k4\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(k9\_funct\_2~X1~k4\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_aofa\_i00~X4~X0~X1~X3){\unicdcdcdhd}(m1\_aofa\_000~X4~X0~(k9\_funct\_2~\\
X1~k4\_numbers)~X3)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_aofa\_i00~X5~X1~(u1\_struct\_0~\\
X0)~(k9\_funct\_2~X1~k4\_numbers)~X4){\unicdbdjdcd}({\unicdcdadad} X6 .  (m3\_aofa\_i00~X6~\\
X0~X1~X3~X4){\unicdbdjdcd}((k21\_aofa\_i00~X1~k4\_numbers~(k2\_binop\_1~(k9\_funct\_2~\\
X1~k4\_numbers)~(u1\_struct\_0~X0)~(k9\_funct\_2~X1~k4\_numbers)~X4~X2~\\
(k55\_aofa\_i00~X0~X1~X3~X4~X5~X6))~X5=k6\_int\_1~(k21\_aofa\_i00~X1~k4\_numbers~\\
X2~X5)~(k3\_funct\_2~(k9\_funct\_2~X1~k4\_numbers)~k4\_numbers~X6~X2)){\unicdcdcdhd}\\
({\unicdcdadad} X7 .  (m1\_subset\_1~X7~X1){\unicdbdjdcd}((X7{\unicdcdgdad}X5){\unicdbdjdcd}(k21\_aofa\_i00~X1~k4\_numbers~\\
(k2\_binop\_1~(k9\_funct\_2~X1~k4\_numbers)~(u1\_struct\_0~X0)~(k9\_funct\_2~\\
X1~k4\_numbers)~X4~X2~(k55\_aofa\_i00~X0~X1~X3~X4~X5~X6))~X7=k21\_aofa\_i00~\\
X1~k4\_numbers~X2~X7))))))))))\end{array}$$
\end{theorem}
\end{document}
