\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{t28\_grcat\_1 (TMavwdR55HGDbRW3mb7xqcTZYgpkx2CgX3b)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_algstr\_0 : {\iota}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_funct\_5 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_funct\_5 : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ k5\_funct\_5 : {\iota}$ be given.
Let $ g2\_algstr\_0 : {{\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 $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}r1\_funct\_2~(u1\_struct\_0~k3\_algstr\_0)~(u1\_struct\_0~k3\_algstr\_0)~\\
np\_\_1~np\_\_1~(k5\_vectsp\_1~k3\_algstr\_0)~k8\_funct\_5\end{array}
\label{hyp:ehgdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdcdcdhd}{({{v1\_classes2}~{X0}})}})}{\unicdbdjdcd}{({{k1\_xboole\_0} \in {X0}})}}}\label{hyp:ehfdgdpfdgmgbgdhdhfgdhcd}
\end{equation}
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}
{{np\_\_1}={{k1\_tarski}~{k1\_xboole\_0}}}\label{hyp:ehedjdpfdgbgchegpfbd}
\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}((k1\_tarski~\\
k1\_xboole\_0 \in X0){\unicdcdcdhd}((k4\_tarski~(k1\_tarski~k1\_xboole\_0)~(k1\_tarski~\\
k1\_xboole\_0) \in X0){\unicdcdcdhd}((k2\_zfmisc\_1~(k1\_tarski~k1\_xboole\_0)~(k1\_tarski~\\
k1\_xboole\_0) \in X0){\unicdcdcdhd}((k9\_funct\_5 \in X0){\unicdcdcdhd}(k8\_funct\_5 \in X0)))))\end{array}
\label{hyp:ehddpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}((k3\_xtuple\_0~\\
X1~X2~X3 \in X0){\unicdcdcdhd}(k6\_xtuple\_0~X1~X2~X3~X4 \in X0))))))\end{array}
\label{hyp:ehbdpfhgchdgbgehpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}((\\
v1\_funct\_2~X4~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))))))){\unicdbdjdcd}((r1\_funct\_2~X0~X1~\\
X2~X3~X4~X5){\unicdbdjded}(X4=X5))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_funct\_5}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((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}({\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  {\unicdcdadad} X5 .  (g2\_algstr\_0~X0~X1~X2=g2\_algstr\_0~X3~X4~X5){\unicdbdjdcd}\\
((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgcdpfbgmghgdhehchpfad}
\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}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\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}
\begin{array}{c}(v1\_funct\_1~k8\_funct\_5){\unicdcdcdhd}((v1\_funct\_2~k8\_funct\_5~np\_\_1~np\_\_1){\unicdcdcdhd}\\
(m1\_subset\_1~k8\_funct\_5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~np\_\_1~np\_\_1))))\end{array}
\label{hyp:egehpflgidpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k5\_vectsp\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k5\_vectsp\_1~X0)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(k5\_vectsp\_1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgfdpfghfgdgehdhahpfbd}
\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}
{{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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k6\_xtuple\_0~X0~X1~\\
X2~X3=k4\_tarski~(k3\_xtuple\_0~X0~X1~X2)~X3\end{array}
\label{hyp:egidpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k4\_struct\_0}~{X0}}={{u2\_struct\_0}~{X0}}})}}}\label{hyp:eggdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_xtuple\_0~X0~X1~X2=k4\_tarski~\\
(k4\_tarski~X0~X1)~X2\end{array}
\label{hyp:egedpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_grcat\_1~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  {\unicdcdaddd} X3 .  \\
{\unicdcdaddd} X4 .  {\unicdcdaddd} X5 .  (X0=k6\_xtuple\_0~X2~X3~X4~X5){\unicdcdcdhd}({\unicdcdaddd} X6 .  \\
((\preoh v2\_struct\_0~X6){\unicdcdcdhd}((v8\_algstr\_0~X6){\unicdcdcdhd}((v13\_algstr\_0~X6){\unicdcdcdhd}((\\
v3\_rlvect\_1~X6){\unicdcdcdhd}((v4\_rlvect\_1~X6){\unicdcdcdhd}(l2\_algstr\_0~X6)))))){\unicdcdcdhd}((\\
X1=X6){\unicdcdcdhd}((X2=u1\_struct\_0~X6){\unicdcdcdhd}((X3=u1\_algstr\_0~X6){\unicdcdcdhd}((X4=k5\_vectsp\_1~\\
X6){\unicdcdcdhd}(X5=k4\_struct\_0~X6)))))))\end{array}
\label{hyp:egcdddpfhgchdgbgehpfbd}
\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 .  (l2\_algstr\_0~X0){\unicdbdjdcd}((v8\_algstr\_0~X0){\unicdbdjdcd}(X0=g2\_algstr\_0~\\
(u1\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u2\_struct\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghidpfbgmghgdhehchpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfhgchdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdaddd} X1 .  \\
(X1 \in X0){\unicdcdcdhd}(r1\_grcat\_1~X1~k3\_algstr\_0))\end{array}$$
\end{theorem}
\end{document}
