\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{t89\_valued\_2 (TMX3FTA4mk8WBDVjcrYxg9KATKEtNkpBCyZ)}
\maketitle
Let $ v1\_valued\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k84\_valued\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_valued\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_valued\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k79\_valued\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k45\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k83\_valued\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k78\_valued\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v7\_valued\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_valued\_0~\\
X2))){\unicdbdjdcd}(k45\_valued\_1~(k18\_valued\_1~X0~X1)~(k18\_valued\_1~X0~X2)=\\
k18\_valued\_1~X0~(k45\_valued\_1~X1~X2))))\end{array}
\label{hyp:ehbdfdpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((v1\_valued\_2~X2){\unicdcdcdhd}((v1\_valued\_2~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X2)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X3))))))){\unicdbdjdcd}(k84\_valued\_2~X0~X1~\\
X2~X3~X4~X5=k83\_valued\_2~X2~X3~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidedpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((v1\_valued\_2~X2){\unicdcdcdhd}((v1\_valued\_2~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X2)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X3))))))){\unicdbdjdcd}(k79\_valued\_2~X0~X1~\\
X2~X3~X4~X5=k78\_valued\_2~X2~X3~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdjdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_xboole\_0~X0~(k3\_xboole\_0~\\
X1~X2)=k3\_xboole\_0~(k3\_xboole\_0~X0~X1)~(k3\_xboole\_0~X0~X2)\end{array}
\label{hyp:mgbdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v7\_valued\_2~\\
X0))){\unicdbdjdcd}(v1\_valued\_0~(k1\_funct\_1~X0~X1))\end{array}
\label{hyp:ggdgedcdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v7\_valued\_2~\\
X0))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_1~\\
X0~X1)))\end{array}
\label{hyp:ggdgedadpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_valued\_2}~{({{k2\_valued\_2}~{X0}})}}}\label{hyp:ggdgcdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((v1\_valued\_2~X2){\unicdcdcdhd}((v1\_valued\_2~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X2)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X3))))))){\unicdbdjdcd}((v1\_funct\_1~(k84\_valued\_2~\\
X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}(m1\_subset\_1~(k84\_valued\_2~X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_xboole\_0~X0~X1)~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~\\
X2)~(k1\_valued\_2~X3)))))))\end{array}
\label{hyp:egehpflgidedpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_valued\_2~X0){\unicdcdcdhd}\\
((v1\_valued\_2~X1){\unicdcdcdhd}(((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~X0){\unicdcdcdhd}(v1\_funct\_1~\\
X2))){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}((v5\_relat\_1~X3~X1){\unicdcdcdhd}(v1\_funct\_1~X3)))))){\unicdbdjdcd}\\
((v1\_relat\_1~(k83\_valued\_2~X0~X1~X2~X3)){\unicdcdcdhd}(v1\_funct\_1~(k83\_valued\_2~\\
X0~X1~X2~X3)))\end{array}
\label{hyp:egehpflgidddpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((v1\_valued\_2~X2){\unicdcdcdhd}((v1\_valued\_2~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X2)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X3))))))){\unicdbdjdcd}((v1\_funct\_1~(k79\_valued\_2~\\
X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}(m1\_subset\_1~(k79\_valued\_2~X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_xboole\_0~X0~X1)~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~\\
X2)~(k1\_valued\_2~X3)))))))\end{array}
\label{hyp:egehpflghdjdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k3\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(X3 \in X1)))\end{array}
\label{hyp:egedpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_valued\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_valued\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~X0){\unicdcdcdhd}(v1\_funct\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_relat\_1~X3){\unicdcdcdhd}((v5\_relat\_1~X3~X1){\unicdcdcdhd}(v1\_funct\_1~X3))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}((X4=k83\_valued\_2~X0~X1~X2~\\
X3){\unicdbdjded}((k9\_xtuple\_0~X4=k3\_xboole\_0~(k9\_xtuple\_0~X2)~(k9\_xtuple\_0~\\
X3)){\unicdcdcdhd}({\unicdcdadad} X5 .  (X5 \in k9\_xtuple\_0~X4){\unicdbdjdcd}(k1\_funct\_1~X4~X5=k18\_valued\_1~\\
(k1\_funct\_1~X2~X5)~(k1\_funct\_1~X3~X5)))))))))\end{array}
\label{hyp:egedhdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_valued\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_valued\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~X0){\unicdcdcdhd}(v1\_funct\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_relat\_1~X3){\unicdcdcdhd}((v5\_relat\_1~X3~X1){\unicdcdcdhd}(v1\_funct\_1~X3))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}((X4=k78\_valued\_2~X0~X1~X2~\\
X3){\unicdbdjded}((k9\_xtuple\_0~X4=k3\_xboole\_0~(k9\_xtuple\_0~X2)~(k9\_xtuple\_0~\\
X3)){\unicdcdcdhd}({\unicdcdadad} X5 .  (X5 \in k9\_xtuple\_0~X4){\unicdbdjdcd}(k1\_funct\_1~X4~X5=k45\_valued\_1~\\
(k1\_funct\_1~X2~X5)~(k1\_funct\_1~X3~X5)))))))))\end{array}
\label{hyp:egedgdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_valued\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v5\_relat\_1~X1~X0){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v7\_valued\_2~X1)))))\end{array}
\label{hyp:dgdgcdbdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehidjdpfghbgmgfhfgegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (v1\_valued\_2~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (v1\_valued\_2~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_valued\_2~X5){\unicdbdjdcd}(\\
{\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X3)))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_funct\_1~X7){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X4)))){\unicdbdjdcd}({\unicdcdadad} X8 .  ((v1\_funct\_1~X8){\unicdcdcdhd}(m1\_subset\_1~\\
X8~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X5)))){\unicdbdjdcd}(k84\_valued\_2~X0~(k3\_xboole\_0~\\
X1~X2)~X3~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~X4)~(k1\_valued\_2~\\
X5)))~X6~(k79\_valued\_2~X1~X2~X4~X5~X7~X8)=k79\_valued\_2~(k3\_xboole\_0~\\
X0~X1)~(k3\_xboole\_0~X0~X2)~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~\\
X3)~(k1\_valued\_2~X4)))~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~\\
X3)~(k1\_valued\_2~X5)))~(k84\_valued\_2~X0~X1~X3~X4~X6~X7)~(k84\_valued\_2~\\
X0~X2~X3~X5~X6~X8)))))))\end{array}$$
\end{theorem}
\end{document}
