\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{t36\_funct\_6 (TMWZgUqKs5oVwBsZYiCaP8Rrsn4y24bmcpL)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_funct\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((X0 \in k4\_card\_3~X1){\unicdbdjded}((k9\_xtuple\_0~\\
X0=k9\_xtuple\_0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
X0~X2 \in k1\_funct\_1~X1~X2)))))\end{array}
\label{hyp:ehjdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}(((X0 \in k9\_xtuple\_0~\\
X2){\unicdcdcdhd}((X3=k1\_funct\_1~X2~X0){\unicdcdcdhd}(X1 \in k9\_xtuple\_0~X3))){\unicdbdjdcd}((k4\_tarski~\\
X0~X1 \in k9\_xtuple\_0~(k2\_funct\_5~X2)){\unicdcdcdhd}((k1\_binop\_1~(k2\_funct\_5~\\
X2)~X0~X1=k1\_funct\_1~X3~X1){\unicdcdcdhd}(k1\_funct\_1~X3~X1 \in k10\_xtuple\_0~(k2\_funct\_5~\\
X2))))))\end{array}
\label{hyp:ehddidpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~(\\
k7\_funct\_6~X0)){\unicdcdcdhd}(v1\_funct\_1~(k7\_funct\_6~X0)))\end{array}
\label{hyp:egehpflghdpfggfhogdgehpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~(\\
k2\_funct\_6~X0)){\unicdcdcdhd}(v1\_funct\_1~(k2\_funct\_6~X0)))\end{array}
\label{hyp:egehpflgcdpfggfhogdgehpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((X1=k7\_funct\_6~X0){\unicdbdjded}((k9\_xtuple\_0~\\
X1=k4\_card\_3~(k2\_funct\_6~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}\\
(v1\_funct\_1~X2)){\unicdbdjdcd}(\preoh (X2 \in k4\_card\_3~(k2\_funct\_6~X0)){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}(\preoh (k1\_funct\_1~X1~X2=X3){\unicdcdcdhd}(\\
(k9\_xtuple\_0~X3=k8\_relat\_1~X0~(k1\_funct\_6~(k10\_xtuple\_0~X0))){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  (X4 \in k9\_xtuple\_0~X3){\unicdbdjdcd}(k1\_funct\_1~X3~X4=k1\_binop\_1~\\
(k2\_funct\_5~X0)~X4~(k1\_funct\_1~X2~X4)))))))))))\end{array}
\label{hyp:eghdpfggfhogdgehpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
k5\_funct\_6~X0~X1~X2=k1\_binop\_1~(k2\_funct\_5~X0)~X1~X2)\end{array}
\label{hyp:egfdpfggfhogdgehpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((X1=k2\_funct\_6~X0){\unicdbdjded}((k9\_xtuple\_0~\\
X1=k8\_relat\_1~X0~(k1\_funct\_6~(k10\_xtuple\_0~X0))){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(X2 \in k8\_relat\_1~X0~(k1\_funct\_6~(k10\_xtuple\_0~X0))){\unicdbdjdcd}(k1\_funct\_1~\\
X1~X2=k9\_xtuple\_0~(k1\_funct\_1~X0~X2))))))\end{array}
\label{hyp:egcdpfggfhogdgehpfgd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfggfhogdgehpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}(((X1 \in k4\_card\_3~(k2\_funct\_6~\\
X2)){\unicdcdcdhd}(X0 \in k9\_xtuple\_0~X1)){\unicdbdjdcd}(k5\_funct\_6~(k7\_funct\_6~X2)~X1~X0=\\
k5\_funct\_6~X2~X0~(k1\_funct\_1~X1~X0))))\end{array}$$
\end{theorem}
\end{document}
