\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{t49\_funct\_5 (TMK67CwVYQtJi49JytomyoVMxD3EaR2HQe2)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_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 $ 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}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\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}((r1\_tarski~(k10\_xtuple\_0~X2)~(k1\_funct\_2~X0~X1)){\unicdbdjdcd}((X0=\\
k1\_xboole\_0){\unicdcdcdid}((k1\_funct\_5~(k2\_funct\_5~X2)=X2){\unicdcdcdhd}(k3\_funct\_5~\\
(k4\_funct\_5~X2)=X2))))\end{array}
\label{hyp:ehedidpfggfhogdgehpffd}
\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}(((k9\_xtuple\_0~\\
X2=k2\_zfmisc\_1~X0~X1){\unicdcdcdhd}((k9\_xtuple\_0~X3=k2\_zfmisc\_1~X0~X1){\unicdcdcdhd}(k3\_funct\_5~\\
X2=k3\_funct\_5~X3))){\unicdbdjdcd}(X2=X3)))\end{array}
\label{hyp:ehedfdpfggfhogdgehpffd}
\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}(((k9\_xtuple\_0~\\
X2=k2\_zfmisc\_1~X0~X1){\unicdcdcdhd}((k9\_xtuple\_0~X3=k2\_zfmisc\_1~X0~X1){\unicdcdcdhd}(k1\_funct\_5~\\
X2=k1\_funct\_5~X3))){\unicdbdjdcd}(X2=X3)))\end{array}
\label{hyp:ehededpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k2\_funct\_5~k1\_xboole\_0=k1\_xboole\_0){\unicdcdcdhd}(k4\_funct\_5~k1\_xboole\_0=\\
k1\_xboole\_0)\end{array}
\label{hyp:ehedddpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_funct\_5~k1\_xboole\_0=k1\_xboole\_0){\unicdcdcdhd}(k3\_funct\_5~k1\_xboole\_0=\\
k1\_xboole\_0)\end{array}
\label{hyp:ehedcdpfggfhogdgehpffd}
\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}((k9\_xtuple\_0~X2=k2\_zfmisc\_1~X0~X1){\unicdbdjdcd}((r1\_tarski~(k10\_xtuple\_0~\\
(k1\_funct\_5~X2))~(k1\_funct\_2~X1~(k10\_xtuple\_0~X2))){\unicdcdcdhd}(r1\_tarski~\\
(k10\_xtuple\_0~(k3\_funct\_5~X2))~(k1\_funct\_2~X0~(k10\_xtuple\_0~X2)))))\end{array}
\label{hyp:ehddfdpfggfhogdgehpffd}
\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}((r1\_tarski~(k10\_xtuple\_0~X2)~(k1\_funct\_2~X0~X1)){\unicdbdjdcd}((k9\_xtuple\_0~\\
(k2\_funct\_5~X2)=k2\_zfmisc\_1~(k9\_xtuple\_0~X2)~X0){\unicdcdcdhd}(k9\_xtuple\_0~\\
(k4\_funct\_5~X2)=k2\_zfmisc\_1~X0~(k9\_xtuple\_0~X2))))\end{array}
\label{hyp:ehcdgdpfggfhogdgehpffd}
\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}((k9\_xtuple\_0~X2=k2\_zfmisc\_1~X0~X1){\unicdbdjdcd}((k2\_zfmisc\_1~X0~X1=\\
k1\_xboole\_0){\unicdcdcdid}((k9\_xtuple\_0~(k1\_funct\_5~X2)=X0){\unicdcdcdhd}(k9\_xtuple\_0~\\
(k3\_funct\_5~X2)=X1))))\end{array}
\label{hyp:ehcdedpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1))\end{array}
\label{hyp:chdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_relat\_1~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k9\_xtuple\_0~X0))\end{array}
\label{hyp:ggdgidpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\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~(\\
k4\_funct\_5~X0)){\unicdcdcdhd}(v1\_funct\_1~(k4\_funct\_5~X0)))\end{array}
\label{hyp:egehpflgedpfggfhogdgehpffd}
\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~(\\
k3\_funct\_5~X0)){\unicdcdcdhd}(v1\_funct\_1~(k3\_funct\_5~X0)))\end{array}
\label{hyp:egehpflgddpfggfhogdgehpffd}
\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\_5~X0)){\unicdcdcdhd}(v1\_funct\_1~(k2\_funct\_5~X0)))\end{array}
\label{hyp:egehpflgcdpfggfhogdgehpffd}
\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~(\\
k1\_funct\_5~X0)){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_5~X0)))\end{array}
\label{hyp:egehpflgbdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~\\
X1~X0)){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~X1~X0))))\end{array}
\label{hyp:dgdgidpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~\\
X1~X0)){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0))))\end{array}
\label{hyp:dgdghdpfchfgmgbgehpfbd}
\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 .  {\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:ehedjdpfggfhogdgehpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((k9\_xtuple\_0~X2=k2\_zfmisc\_1~X0~X1){\unicdbdjdcd}((k2\_funct\_5~(k1\_funct\_5~\\
X2)=X2){\unicdcdcdhd}(k4\_funct\_5~(k3\_funct\_5~X2)=X2)))\end{array}$$
\end{theorem}
\end{document}
