\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{l36\_classes1 (TMHYhCqHZamFwMsEAva96GhPDQMegQvFd9F)}
\maketitle
Let $ k4\_classes1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 : \\
\iota{\unicdbdjdcd}\iota .  ({\unicdcdadad} X4 .  (v3\_ordinal1~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (X5=X3~X4){\unicdbdjded}\\
({\unicdcdaddd} X6 .  ((v5\_ordinal1~X6){\unicdcdcdhd}((v1\_relat\_1~X6){\unicdcdcdhd}(v1\_funct\_1~\\
X6))){\unicdcdcdhd}((X5=k1\_ordinal2~X6){\unicdcdcdhd}((k9\_xtuple\_0~X6=k1\_ordinal1~X4){\unicdcdcdhd}\\
((k1\_funct\_1~X6~k1\_xboole\_0=X2){\unicdcdcdhd}(({\unicdcdadad} X7 .  (v3\_ordinal1~X7){\unicdbdjdcd}\\
((k1\_ordinal1~X7 \in k1\_ordinal1~X4){\unicdbdjdcd}(k1\_funct\_1~X6~(k1\_ordinal1~\\
X7)=X1~X7~(k1\_funct\_1~X6~X7)))){\unicdcdcdhd}({\unicdcdadad} X7 .  (v3\_ordinal1~X7){\unicdbdjdcd}\\
(((X7 \in k1\_ordinal1~X4){\unicdcdcdhd}(v4\_ordinal1~X7)){\unicdbdjdcd}((X7=k1\_xboole\_0){\unicdcdcdid}\\
(k1\_funct\_1~X6~X7=X0~X7~(k5\_relat\_1~X6~X7)))))))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(v3\_ordinal1~X4){\unicdbdjdcd}(X3~(k1\_ordinal1~X4)=X1~X4~(X3~X4)))\end{array}
\label{hyp:dhjdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 : \\
\iota{\unicdbdjdcd}\iota .  ({\unicdcdadad} X4 .  (v3\_ordinal1~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (X5=X3~X4){\unicdbdjded}\\
({\unicdcdaddd} X6 .  ((v5\_ordinal1~X6){\unicdcdcdhd}((v1\_relat\_1~X6){\unicdcdcdhd}(v1\_funct\_1~\\
X6))){\unicdcdcdhd}((X5=k1\_ordinal2~X6){\unicdcdcdhd}((k9\_xtuple\_0~X6=k1\_ordinal1~X4){\unicdcdcdhd}\\
((k1\_funct\_1~X6~k1\_xboole\_0=X2){\unicdcdcdhd}(({\unicdcdadad} X7 .  (v3\_ordinal1~X7){\unicdbdjdcd}\\
((k1\_ordinal1~X7 \in k1\_ordinal1~X4){\unicdbdjdcd}(k1\_funct\_1~X6~(k1\_ordinal1~\\
X7)=X1~X7~(k1\_funct\_1~X6~X7)))){\unicdcdcdhd}({\unicdcdadad} X7 .  (v3\_ordinal1~X7){\unicdbdjdcd}\\
(((X7 \in k1\_ordinal1~X4){\unicdcdcdhd}(v4\_ordinal1~X7)){\unicdbdjdcd}((X7=k1\_xboole\_0){\unicdcdcdid}\\
(k1\_funct\_1~X6~X7=X0~X7~(k5\_relat\_1~X6~X7)))))))))))){\unicdbdjdcd}(X3~k1\_xboole\_0=\\
X2)\end{array}
\label{hyp:dhidpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X3 : \iota{\unicdbdjdcd}\\
\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 : \iota{\unicdbdjdcd}\iota .  (({\unicdcdadad} X6 .  (v3\_ordinal1~\\
X6){\unicdbdjdcd}({\unicdcdadad} X7 .  (X7=X5~X6){\unicdbdjded}({\unicdcdaddd} X8 .  ((v5\_ordinal1~X8){\unicdcdcdhd}((\\
v1\_relat\_1~X8){\unicdcdcdhd}(v1\_funct\_1~X8))){\unicdcdcdhd}((X7=k1\_ordinal2~X8){\unicdcdcdhd}((k9\_xtuple\_0~\\
X8=k1\_ordinal1~X6){\unicdcdcdhd}((k1\_funct\_1~X8~k1\_xboole\_0=X4){\unicdcdcdhd}(({\unicdcdadad} X9 .  \\
(v3\_ordinal1~X9){\unicdbdjdcd}((k1\_ordinal1~X9 \in k1\_ordinal1~X6){\unicdbdjdcd}(k1\_funct\_1~\\
X8~(k1\_ordinal1~X9)=X3~X9~(k1\_funct\_1~X8~X9)))){\unicdcdcdhd}({\unicdcdadad} X9 .  (v3\_ordinal1~\\
X9){\unicdbdjdcd}(((X9 \in k1\_ordinal1~X6){\unicdcdcdhd}(v4\_ordinal1~X9)){\unicdbdjdcd}((X9=k1\_xboole\_0){\unicdcdcdid}\\
(k1\_funct\_1~X8~X9=X2~X9~(k5\_relat\_1~X8~X9)))))))))))){\unicdcdcdhd}(((X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
(v4\_ordinal1~X1)){\unicdcdcdhd}((k9\_xtuple\_0~X0=X1){\unicdcdcdhd}({\unicdcdadad} X6 .  (v3\_ordinal1~\\
X6){\unicdbdjdcd}((X6 \in X1){\unicdbdjdcd}(k1\_funct\_1~X0~X6=X5~X6)))))){\unicdbdjdcd}(X5~X1=X2~X1~X0)\end{array}
\label{hyp:dhbdadpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=k4\_classes1~X0){\unicdbdjded}\\
({\unicdcdaddd} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v5\_ordinal1~\\
X2))){\unicdcdcdhd}((X1=k1\_ordinal2~X2){\unicdcdcdhd}((k9\_xtuple\_0~X2=k1\_ordinal1~X0){\unicdcdcdhd}\\
((k1\_funct\_1~X2~k1\_xboole\_0=k1\_xboole\_0){\unicdcdcdhd}(({\unicdcdadad} X3 .  (v3\_ordinal1~\\
X3){\unicdbdjdcd}((k1\_ordinal1~X3 \in k1\_ordinal1~X0){\unicdbdjdcd}(k1\_funct\_1~X2~(k1\_ordinal1~\\
X3)=k9\_setfam\_1~(k1\_funct\_1~X2~X3)))){\unicdcdcdhd}({\unicdcdadad} X3 .  (v3\_ordinal1~\\
X3){\unicdbdjdcd}(((X3 \in k1\_ordinal1~X0){\unicdcdcdhd}(v4\_ordinal1~X3)){\unicdbdjdcd}((X3=k1\_xboole\_0){\unicdcdcdid}\\
(k1\_funct\_1~X2~X3=k3\_tarski~(k10\_xtuple\_0~(k5\_relat\_1~X2~X3))))))))))))\end{array}
\label{hyp:eggdpfdgmgbgdhdhfgdhbd}
\end{equation}
\begin{theorem}\label{thm:mgddgdpfdgmgbgdhdhfgdhbd}
$$\begin{array}{c}(k4\_classes1~k1\_xboole\_0=k1\_xboole\_0){\unicdcdcdhd}(({\unicdcdadad} X0 .  (v3\_ordinal1~\\
X0){\unicdbdjdcd}(k4\_classes1~(k1\_ordinal1~X0)=k9\_setfam\_1~(k4\_classes1~\\
X0))){\unicdcdcdhd}({\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v5\_ordinal1~X1))){\unicdbdjdcd}(((v4\_ordinal1~X0){\unicdcdcdhd}\\
((k9\_xtuple\_0~X1=X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (v3\_ordinal1~X2){\unicdbdjdcd}((X2 \in X0){\unicdbdjdcd}\\
(k1\_funct\_1~X1~X2=k4\_classes1~X2))))){\unicdbdjdcd}((X0=k1\_xboole\_0){\unicdcdcdid}(k4\_classes1~\\
X0=k3\_tarski~(k10\_xtuple\_0~X1)))))))\end{array}$$
\end{theorem}
\end{document}
