\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{t68\_valued\_2 (TMHn3dMH6TmUgk5jsNJgEE99rRc4nW4DmwW)}
\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 $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k63\_valued\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k30\_valued\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_valued\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_valued\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_valued\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k24\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k62\_valued\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k15\_valued\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_valued\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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}\\
((k9\_xtuple\_0~(k30\_valued\_1~X0)=k9\_xtuple\_0~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
k1\_funct\_1~(k30\_valued\_1~X0)~X1=k4\_xcmplx\_0~(k1\_funct\_1~X0~X1)))\end{array}
\label{hyp:ehidpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~X1))){\unicdbdjdcd}(k24\_valued\_1~(k30\_valued\_1~\\
X1)~X0=k24\_valued\_1~X1~(k4\_xcmplx\_0~X0)))\end{array}
\label{hyp:ehcdcdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_valued\_2~X1){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_valued\_0~X3))))){\unicdbdjdcd}\\
(k63\_valued\_2~X0~X1~X2~X3=k62\_valued\_2~X1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdddpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_valued\_2~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}(k16\_valued\_2~\\
X0~X1~X2=k15\_valued\_2~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdgdpfghbgmgfhfgegpfcd}
\end{equation}
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}\\
(k30\_valued\_1~(k30\_valued\_1~X0)=X0)\end{array}
\label{hyp:jgogghpgmgfhehjgghfgogfgdhdhpflgddadpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~\\
X0))){\unicdbdjdcd}(v1\_xcmplx\_0~(k1\_funct\_1~X0~X1))\end{array}
\label{hyp:ggdggdbdpfghbgmgfhfgegpfad}
\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 .  ((v1\_valued\_2~X1){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_valued\_0~X3))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k63\_valued\_2~X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k63\_valued\_2~\\
X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_xboole\_0~X0~(k9\_xtuple\_0~\\
X3))~(k2\_valued\_2~(k1\_valued\_2~X1))))))\end{array}
\label{hyp:egehpflggdddpfghbgmgfhfgegpfcd}
\end{equation}
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}\\
((v1\_relat\_1~(k30\_valued\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k30\_valued\_1~\\
X0)){\unicdcdcdhd}(v1\_valued\_0~(k30\_valued\_1~X0))))\end{array}
\label{hyp:egehpflgddadpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_valued\_2~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k16\_valued\_2~X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k16\_valued\_2~X0~X1~X2)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(k2\_valued\_2~(k1\_valued\_2~X1))))))\end{array}
\label{hyp:egehpflgbdgdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v7\_valued\_2~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~(k15\_valued\_2~X0)){\unicdcdcdhd}(v1\_funct\_1~(k15\_valued\_2~X0)))\end{array}
\label{hyp:egehpflgbdfdpfghbgmgfhfgegpfcd}
\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\_relat\_1~X1){\unicdcdcdhd}((\\
v5\_relat\_1~X1~X0){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_valued\_0~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}((X3=k62\_valued\_2~X0~X1~X2){\unicdbdjded}((k9\_xtuple\_0~\\
X3=k3\_xboole\_0~(k9\_xtuple\_0~X1)~(k9\_xtuple\_0~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(X4 \in k9\_xtuple\_0~X3){\unicdbdjdcd}(k1\_funct\_1~X3~X4=k24\_valued\_1~(k1\_funct\_1~\\
X1~X4)~(k1\_funct\_1~X2~X4))))))))\end{array}
\label{hyp:egedddpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v7\_valued\_2~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((X1=k15\_valued\_2~\\
X0){\unicdbdjded}((k9\_xtuple\_0~X1=k9\_xtuple\_0~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~\\
X1){\unicdbdjdcd}(k1\_funct\_1~X1~X2=k30\_valued\_1~(k1\_funct\_1~X0~X2))))))\end{array}
\label{hyp:egddddpfghbgmgfhfgegpfcd}
\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 .  {\unicdcdadad} X1 .  (v1\_valued\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v1\_funct\_1~X2){\unicdbdjdcd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v7\_valued\_2~X2))))\end{array}
\label{hyp:dgdgcdidpfghbgmgfhfgegpfcd}
\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:ehgdidpfghbgmgfhfgegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_valued\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_valued\_0~X3))){\unicdbdjdcd}(k63\_valued\_2~\\
X0~X1~X2~(k30\_valued\_1~X3)=k63\_valued\_2~X0~(k2\_valued\_2~(k1\_valued\_2~\\
X1))~(k16\_valued\_2~X0~X1~X2)~X3)))\end{array}$$
\end{theorem}
\end{document}
