\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{t75\_memstr\_0 (TMNGR4wUMsCUe6mdAuhHtZyXhoarQniVbof)}
\maketitle
Let $ v1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_memstr\_0 : {{\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\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k11\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}(v1\_funct\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v5\_funct\_1~X2~X1)))){\unicdbdjdcd}(X2 \in k8\_card\_3~\\
X1))\end{array}
\label{hyp:ehbdadddpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_setfam\_1~X0){\unicdcdcdhd}((v2\_memstr\_0~X1~X0){\unicdcdcdhd}\\
(l1\_memstr\_0~X1~X0))){\unicdbdjdcd}((v1\_relat\_1~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}((v2\_relat\_1~\\
(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k2\_memstr\_0~X0~X1)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}((v1\_funct\_1~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}(v1\_partfun1~(k2\_memstr\_0~\\
X0~X1)~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:ggdgddpfngfgngdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_setfam\_1~X0){\unicdcdcdhd}(l1\_memstr\_0~X1~X0)){\unicdbdjdcd}\\
((v1\_relat\_1~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k2\_memstr\_0~\\
X0~X1)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
(k2\_memstr\_0~X0~X1)~(u1\_struct\_0~X1)))))\end{array}
\label{hyp:egehpflgcdpfngfgngdhehchpfad}
\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\_memstr\_0~X1~X0)){\unicdbdjdcd}(k11\_memstr\_0~X0~X1=ReplSep~(toset~({\uniddcgcg} X2 : \\
\iota .  m1\_subset\_1~X2~(k8\_card\_3~(k2\_memstr\_0~X0~X1))))~({\uniddcgcg} X2 : \\
\iota .  v1\_finset\_1~X2)~({\uniddcgcg} X2 : \iota .  X2)))\end{array}
\label{hyp:egbdgdpfngfgngdhehchpfad}
\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}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v5\_funct\_1~X2~X1))){\unicdbdjdcd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}\\
(v1\_funct\_1~X2))))\end{array}
\label{hyp:dgdgbdadpfggfhogdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdfdpfngfgngdhehchpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_memstr\_0~X1~X0){\unicdcdcdhd}\\
(l1\_memstr\_0~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~\\
X0~X1)){\unicdcdcdhd}(v1\_finset\_1~X2))))){\unicdbdjdcd}(X2 \in k11\_memstr\_0~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
