\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{t32\_funct\_3 (TMR74m9dPB2UrBdgknrJdsn6z7pyS3LJiLP)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\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}(r1\_tarski~(k10\_xtuple\_0~\\
(k1\_funct\_3~X0))~(k1\_zfmisc\_1~(k10\_xtuple\_0~X0)))\end{array}
\label{hyp:ehjdpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(((\\
r1\_tarski~X0~(k9\_xtuple\_0~X1)){\unicdcdcdhd}(v2\_funct\_1~X1)){\unicdbdjdcd}(k8\_relat\_1~\\
X1~(k7\_relat\_1~X1~X0)=X0))\end{array}
\label{hyp:ehjdedpfggfhogdgehpfbd}
\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~X0~(k9\_xtuple\_0~X2)){\unicdcdcdhd}(r1\_tarski~(k7\_relat\_1~\\
X2~X0)~X1)){\unicdbdjdcd}(r1\_tarski~X0~(k8\_relat\_1~X2~X1)))\end{array}
\label{hyp:ehjdddpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}(({\unicdcdadad} X1 .  r1\_tarski~\\
(k8\_relat\_1~X0~(k7\_relat\_1~X0~X1))~X1){\unicdbdjdcd}(v2\_funct\_1~X0))\end{array}
\label{hyp:ehidddpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((v2\_funct\_1~\\
X1){\unicdbdjdcd}(r1\_tarski~(k8\_relat\_1~X1~(k7\_relat\_1~X1~X0))~X0))\end{array}
\label{hyp:ehidcdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((r1\_tarski~\\
X0~(k10\_xtuple\_0~X1)){\unicdbdjdcd}(k7\_relat\_1~X1~(k8\_relat\_1~X1~X0)=X0))\end{array}
\label{hyp:ehhdhdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(r1\_tarski~\\
(k7\_relat\_1~X1~(k8\_relat\_1~X1~X0))~X0)\end{array}
\label{hyp:ehhdfdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_tarski~\\
X1~(k1\_zfmisc\_1~(k9\_xtuple\_0~X0))){\unicdbdjdcd}(r1\_tarski~(k8\_relat\_1~(k3\_funct\_3~\\
X0)~X1)~(k7\_relat\_1~(k1\_funct\_3~X0)~X1)))\end{array}
\label{hyp:ehddbdpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((v2\_funct\_1~\\
X1){\unicdbdjdcd}(k7\_relat\_1~(k3\_funct\_3~X1)~X0=k8\_relat\_1~(k1\_funct\_3~X1)~\\
X0))\end{array}
\label{hyp:ehddadpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((r1\_tarski~\\
(k10\_xtuple\_0~X0)~(k9\_xtuple\_0~X1)){\unicdbdjdcd}(k9\_xtuple\_0~(k3\_relat\_1~\\
X0~X1)=k9\_xtuple\_0~X0)))\end{array}
\label{hyp:ehcdhdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v2\_funct\_1~X0){\unicdbdjded}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
(v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}(((r1\_tarski~(k10\_xtuple\_0~\\
X1)~(k9\_xtuple\_0~X0)){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~X2)~(k9\_xtuple\_0~\\
X0)){\unicdcdcdhd}((k9\_xtuple\_0~X1=k9\_xtuple\_0~X2){\unicdcdcdhd}(k3\_relat\_1~X1~X0=k3\_relat\_1~\\
X2~X0)))){\unicdbdjdcd}(X1=X2)))))\end{array}
\label{hyp:ehcdhdpfggfhogdgehpfbd}
\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}(((v2\_funct\_1~(k3\_relat\_1~X1~\\
X0)){\unicdcdcdhd}(k10\_xtuple\_0~X1=k9\_xtuple\_0~X0)){\unicdbdjdcd}((v2\_funct\_1~X1){\unicdcdcdhd}(v2\_funct\_1~\\
X0))))\end{array}
\label{hyp:ehcdgdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~(\\
k1\_funct\_3~X0)){\unicdcdcdhd}((v1\_funct\_2~(k1\_funct\_3~X0)~(k1\_zfmisc\_1~(k9\_xtuple\_0~\\
X0))~(k1\_zfmisc\_1~(k10\_xtuple\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~(k1\_funct\_3~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_zfmisc\_1~(k9\_xtuple\_0~X0))~\\
(k1\_zfmisc\_1~(k10\_xtuple\_0~X0)))))))\end{array}
\label{hyp:ehbdjdpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}(k9\_xtuple\_0~\\
(k3\_relat\_1~X0~X1)=k8\_relat\_1~X0~(k9\_xtuple\_0~X1)))\end{array}
\label{hyp:ehbdedhdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_relat\_1~\\
X2){\unicdbdjdcd}(k8\_relat\_1~(k3\_relat\_1~X1~X2)~X0=k8\_relat\_1~X1~(k8\_relat\_1~\\
X2~X0)))\end{array}
\label{hyp:ehbdedgdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}(k8\_relat\_1~X0~(k10\_xtuple\_0~X0)=\\
k9\_xtuple\_0~X0)\end{array}
\label{hyp:ehbdddedpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}(r1\_tarski~(k8\_relat\_1~\\
X1~X0)~(k9\_xtuple\_0~X1))\end{array}
\label{hyp:ehbdddcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_relat\_1~\\
X2){\unicdbdjdcd}(k7\_relat\_1~(k3\_relat\_1~X1~X2)~X0=k7\_relat\_1~X2~(k7\_relat\_1~\\
X1~X0)))\end{array}
\label{hyp:ehbdcdgdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}(k7\_relat\_1~X0~(k9\_xtuple\_0~X0)=k10\_xtuple\_0~\\
X0)\end{array}
\label{hyp:ehbdbdddpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(r1\_tarski~\\
(k7\_relat\_1~(k1\_funct\_3~X1)~X0)~(k1\_zfmisc\_1~(k10\_xtuple\_0~X1)))\end{array}
\label{hyp:ehbdadpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\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\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}((v1\_relat\_1~(k3\_relat\_1~X0~\\
X1)){\unicdcdcdhd}(v1\_funct\_1~(k3\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdgcdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k3\_relat\_1}~{X0}}~{X1}})}}}}\label{hyp:egehpflgddpfchfgmgbgehpfbd}
\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\_3~X0)){\unicdcdcdhd}(v1\_funct\_1~(k3\_funct\_3~X0)))\end{array}
\label{hyp:egehpflgddpfggfhogdgehpfdd}
\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\_3~X0)){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_3~X0)))\end{array}
\label{hyp:egehpflgbdpfggfhogdgehpfdd}
\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=k3\_funct\_3~X0){\unicdbdjded}((k9\_xtuple\_0~\\
X1=k1\_zfmisc\_1~(k10\_xtuple\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (r1\_tarski~X2~\\
(k10\_xtuple\_0~X0)){\unicdbdjdcd}(k1\_funct\_1~X1~X2=k8\_relat\_1~X0~X2)))))\end{array}
\label{hyp:egcdpfggfhogdgehpfdd}
\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=k1\_funct\_3~X0){\unicdbdjded}((k9\_xtuple\_0~\\
X1=k1\_zfmisc\_1~(k9\_xtuple\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (r1\_tarski~X2~(\\
k9\_xtuple\_0~X0)){\unicdbdjdcd}(k1\_funct\_1~X1~X2=k7\_relat\_1~X0~X2)))))\end{array}
\label{hyp:egbdpfggfhogdgehpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfggfhogdgehpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_funct\_1~\\
X0){\unicdbdjdcd}(r1\_tarski~(k7\_relat\_1~(k1\_funct\_3~X0)~X1)~(k8\_relat\_1~(k3\_funct\_3~\\
X0)~X1)))\end{array}$$
\end{theorem}
\end{document}
