\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{t17\_amistd\_1 (TMbWtF5GZm1cqHEDKVzBTRtLurWwZXVWhwG)}
\maketitle
Let $ v1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~(u1\_struct\_0~(k1\_extpro\_1~X0))){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~X0~(k1\_extpro\_1~X0))){\unicdcdcdhd}(v1\_partfun1~\\
X1~(u1\_struct\_0~(k1\_extpro\_1~X0))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_compos\_1~(k1\_extpro\_1~X0))){\unicdbdjdcd}(k2\_extpro\_1~X0~(k1\_extpro\_1~\\
X0)~X2~X1=X1)))\end{array}
\label{hyp:ehbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}((v2\_memstr\_0~(k1\_extpro\_1~X0)~\\
X0){\unicdcdcdhd}(v1\_extpro\_1~(k1\_extpro\_1~X0)~X0))\end{array}
\label{hyp:ggdgcdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}((v1\_extpro\_1~(k1\_extpro\_1~X0)~\\
X0){\unicdcdcdhd}(l1\_extpro\_1~(k1\_extpro\_1~X0)~X0))\end{array}
\label{hyp:egehpflgbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_memstr\_0~X1~X0){\unicdcdcdhd}\\
(l1\_extpro\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_compos\_1~\\
X1)){\unicdbdjdcd}((v2\_extpro\_1~X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((\\
v4\_relat\_1~X3~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_funct\_1~\\
X3~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}(v1\_partfun1~X3~(u1\_struct\_0~X1)))))){\unicdbdjdcd}\\
(k2\_extpro\_1~X0~X1~X2~X3=X3)))))\end{array}
\label{hyp:egddpffgihehahchpgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfbgngjgdhehegpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_compos\_1~\\
(k1\_extpro\_1~X0))){\unicdbdjdcd}(v2\_extpro\_1~X1~X0~(k1\_extpro\_1~X0)))\end{array}$$
\end{theorem}
\end{document}
