\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{t37\_grcat\_1 (TMVeGr5snygHhN31zJapDAGLCB8yj9bpExB)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_algstr\_0 : {\iota}$ be given.
Let $ k26\_grcat\_1 : {{\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k17\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_funct\_5 : {\iota}$ be given.
Let $ k7\_funct\_5 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g1\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v13\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_algstr\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_algstr\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k25\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_funct\_5 : {\iota}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k24\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k23\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k22\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_cat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}(k3\_algstr\_0 \in \\
k17\_grcat\_1~X0)\end{array}
\label{hyp:ehcdjdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_1}}}}\label{hyp:dhahdgbdpfcgpgpgmgfg}
\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}
{{k9\_funct\_5}={k7\_funct\_5}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0))))){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))))){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)~X1)))))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  (g1\_cat\_1~X0~X1~X2~\\
X3~X4=g1\_cat\_1~X5~X6~X7~X8~X9){\unicdbdjdcd}((X0=X5){\unicdcdcdhd}((X1=X6){\unicdcdcdhd}((X2=X7){\unicdcdcdhd}((X3=\\
X8){\unicdcdcdhd}(X4=X9))))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v13\_struct\_0}~{k3\_algstr\_0}}~{np\_\_1}})}{\unicdcdcdhd}{({{v8\_algstr\_0}~{k3\_algstr\_0}})}}\label{hyp:ggdgjdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(g2\_algstr\_0~X0~X1~X2)){\unicdcdcdhd}(v8\_algstr\_0~(g2\_algstr\_0~\\
X0~X1~X2)))\end{array}
\label{hyp:ggdggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v2\_rlvect\_1}~{k3\_algstr\_0}}\label{hyp:ggdgcdpfbgmghgdhehchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v3\_rlvect\_1~k3\_algstr\_0){\unicdcdcdhd}((v4\_rlvect\_1~k3\_algstr\_0){\unicdcdcdhd}((v1\_algstr\_1~\\
k3\_algstr\_0){\unicdcdcdhd}(v4\_algstr\_1~k3\_algstr\_0)))\end{array}
\label{hyp:ggdgbdpfbgmghgdhehchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k25\_grcat\_1~X0)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k25\_grcat\_1~X0)){\unicdcdcdhd}(v1\_cat\_1~\\
(k25\_grcat\_1~X0))))\end{array}
\label{hyp:ggdgbdddpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}(v3\_grcat\_1~\\
(k17\_grcat\_1~X0))\end{array}
\label{hyp:ggdgbdcdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k17\_grcat\_1~X0))\end{array}
\label{hyp:ggdgbdbdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k9\_funct\_5){\unicdcdcdhd}((v1\_funct\_2~k9\_funct\_5~(k2\_zfmisc\_1~\\
np\_\_1~np\_\_1)~np\_\_1){\unicdcdcdhd}(m1\_subset\_1~k9\_funct\_5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~np\_\_1~np\_\_1)~np\_\_1))))\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_funct\_5}}~{np\_\_1}}\label{hyp:egehpflgfdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
{{l2\_algstr\_0}~{k3\_algstr\_0}}\label{hyp:egehpflgddpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k25\_grcat\_1~X0)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k25\_grcat\_1~X0)){\unicdcdcdhd}((v1\_cat\_1~\\
(k25\_grcat\_1~X0)){\unicdcdcdhd}(l1\_cat\_1~(k25\_grcat\_1~X0)))))\end{array}
\label{hyp:egehpflgcdfdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k24\_grcat\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~(k24\_grcat\_1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k18\_grcat\_1~X0)~(k18\_grcat\_1~X0))~\\
(k18\_grcat\_1~X0)))))\end{array}
\label{hyp:egehpflgcdedpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k23\_grcat\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k23\_grcat\_1~X0)~(k18\_grcat\_1~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k23\_grcat\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k18\_grcat\_1~X0)~X0)))))\end{array}
\label{hyp:egehpflgcdddpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k22\_grcat\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k22\_grcat\_1~X0)~(k18\_grcat\_1~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k22\_grcat\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k18\_grcat\_1~X0)~X0)))))\end{array}
\label{hyp:egehpflgcdcdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k3\_algstr\_0}={{{{g2\_algstr\_0}~{np\_\_1}}~{k9\_funct\_5}}~{k5\_funct\_5}}}\label{hyp:egjdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}(k26\_grcat\_1~\\
X0=ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(u1\_struct\_0~(k25\_grcat\_1~\\
X0))))~({\uniddcgcg} X1 : \iota .  {\unicdcdaddd} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~\\
X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}\\
(l2\_algstr\_0~X2)))))){\unicdcdcdhd}(X1=X2))~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:egddbdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}(k25\_grcat\_1~\\
X0=g1\_cat\_1~(k17\_grcat\_1~X0)~(k18\_grcat\_1~(k17\_grcat\_1~X0))~(\\
k22\_grcat\_1~(k17\_grcat\_1~X0))~(k23\_grcat\_1~(k17\_grcat\_1~X0))~\\
(k24\_grcat\_1~(k17\_grcat\_1~X0)))\end{array}
\label{hyp:egddadpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_algstr\_0~X0){\unicdbdjdcd}((v13\_struct\_0~X0~np\_\_1){\unicdbdjdcd}((v13\_struct\_0~\\
X0~np\_\_1){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}(v4\_rlvect\_1~X0))))))\end{array}
\label{hyp:dgdghdpfbgmghgdhehchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_cat\_1~X0){\unicdbdjdcd}((v1\_cat\_1~X0){\unicdbdjdcd}(X0=g1\_cat\_1~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~X0)~(u1\_cat\_1~\\
X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfhgchdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}(k3\_algstr\_0 \in \\
k26\_grcat\_1~X0)\end{array}$$
\end{theorem}
\end{document}
