\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{t6\_msinst\_1 (TMRRf9SmGobLcLvKWYeR8ZDjY47ye1NQDUn)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_msinst\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_msinst\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_msinst\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funcop\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ u2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdbdjdcd}((\preoh v2\_struct\_0~(k4\_msinst\_1~\\
X0~X1)){\unicdcdcdhd}((v2\_altcat\_1~(k4\_msinst\_1~X0~X1)){\unicdcdcdhd}((v6\_altcat\_1~(k4\_msinst\_1~\\
X0~X1)){\unicdcdcdhd}((v11\_altcat\_1~(k4\_msinst\_1~X0~X1)){\unicdcdcdhd}(v12\_altcat\_1~(k4\_msinst\_1~\\
X0~X1))))))\end{array}
\label{hyp:ggdgddpfngdhjgogdhehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k2\_msinst\_1~\\
X0~X1))\end{array}
\label{hyp:ggdgcdpfngdhjgogdhehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}((v6\_altcat\_1~X2){\unicdcdcdhd}(l2\_altcat\_1~X2))){\unicdbdjdcd}((X2=k4\_msinst\_1~\\
X0~X1){\unicdbdjded}((u1\_struct\_0~X2=k2\_msinst\_1~X0~X1){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k2\_msinst\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k2\_msinst\_1~\\
X0~X1)){\unicdbdjdcd}(k1\_binop\_1~(u1\_altcat\_1~X2)~X3~X4=k3\_msinst\_1~X0~X1~X3~\\
X4))){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}((v1\_funct\_1~\\
X6){\unicdcdcdhd}(v1\_funcop\_1~X6))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_relat\_1~X7){\unicdcdcdhd}((v1\_funct\_1~\\
X7){\unicdcdcdhd}(v1\_funcop\_1~X7))){\unicdbdjdcd}(((X6 \in k1\_binop\_1~(u1\_altcat\_1~X2)~X3~\\
X4){\unicdcdcdhd}(X7 \in k1\_binop\_1~(u1\_altcat\_1~X2)~X4~X5)){\unicdbdjdcd}(k1\_binop\_1~(k4\_altcat\_1~\\
(u1\_struct\_0~X2)~(u1\_altcat\_1~X2)~(u2\_altcat\_1~X2)~X3~X4~X5)~X7~X6=\\
k8\_pboole~X6~X7))))))))))))\end{array}
\label{hyp:egedpfngdhjgogdhehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (X2=k2\_msinst\_1~\\
X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  ((v3\_msualg\_1~X4~X0){\unicdcdcdhd}\\
((v1\_msualg\_6~X4~X0){\unicdcdcdhd}(l3\_msualg\_1~X4~X0))){\unicdcdcdhd}((X3=X4){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(k10\_xtuple\_0~(u3\_msualg\_1~X0~X4))){\unicdbdjdcd}(r1\_tarski~\\
X5~X1)))))))\end{array}
\label{hyp:egcdpfngdhjgogdhehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfngdhjgogdhehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}((v2\_altcat\_1~X2){\unicdcdcdhd}((v11\_altcat\_1~X2){\unicdcdcdhd}((v12\_altcat\_1~X2){\unicdcdcdhd}\\
(l2\_altcat\_1~X2))))){\unicdbdjdcd}((X2=k4\_msinst\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X2)){\unicdbdjdcd}((v3\_msualg\_1~X3~X1){\unicdcdcdhd}((v1\_msualg\_6~X3~X1){\unicdcdcdhd}\\
(l3\_msualg\_1~X3~X1)))))))\end{array}$$
\end{theorem}
\end{document}
