\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{t24\_mssubfam (TMYjKSs6BYoPkzKaRJ3QF9aRxEXnMpd2QfA)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funcop\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\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}((v1\_finset\_1~\\
(k9\_xtuple\_0~X0)){\unicdbdjdcd}(v1\_finset\_1~(k10\_xtuple\_0~X0)))\end{array}
\label{hyp:ehidpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~X1){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_partfun1~X2~X1){\unicdcdcdhd}(v1\_funcop\_1~X2))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}(((X0 \in X1){\unicdcdcdhd}(X3=\\
k1\_funct\_1~X2~X0)){\unicdbdjdcd}(k1\_funct\_1~(k2\_funct\_6~X2)~X0=k9\_xtuple\_0~\\
X3)))\end{array}
\label{hyp:ehbdedpfngdhdhfhcgggbgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~X1){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_partfun1~X2~X1){\unicdcdcdhd}(v1\_funcop\_1~X2))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}(((X0 \in X1){\unicdcdcdhd}(X3=\\
k1\_funct\_1~X2~X0)){\unicdbdjdcd}(k1\_funct\_1~(k3\_funct\_6~X2)~X0=k10\_xtuple\_0~\\
X3)))\end{array}
\label{hyp:ehbdddpfngdhdhfhcgggbgng}
\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\_funcop\_1~\\
X0))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_1~\\
X0~X1)))\end{array}
\label{hyp:ggdgidpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_funcop\_1~X1))))){\unicdbdjdcd}(\\
(v1\_relat\_1~(k3\_funct\_6~X1)){\unicdcdcdhd}((v4\_relat\_1~(k3\_funct\_6~X1)~X0){\unicdcdcdhd}\\
(v1\_funct\_1~(k3\_funct\_6~X1))))\end{array}
\label{hyp:ggdgcdpfngdhdhfhcgggbgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_funcop\_1~X1))))){\unicdbdjdcd}(\\
(v1\_relat\_1~(k2\_funct\_6~X1)){\unicdcdcdhd}((v4\_relat\_1~(k2\_funct\_6~X1)~X0){\unicdcdcdhd}\\
(v1\_funct\_1~(k2\_funct\_6~X1))))\end{array}
\label{hyp:ggdgbdpfngdhdhfhcgggbgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
v1\_funct\_1~X1))){\unicdbdjdcd}((v2\_finset\_1~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}(v1\_finset\_1~\\
(k1\_funct\_1~X1~X2))))\end{array}
\label{hyp:egfdpfggjgogdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfngdhdhfhcgggbgng}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_funcop\_1~X1))))){\unicdbdjdcd}(\\
(v2\_finset\_1~(k2\_funct\_6~X1)){\unicdbdjdcd}(v2\_finset\_1~(k3\_funct\_6~X1)))\end{array}$$
\end{theorem}
\end{document}
