\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{t16\_memstr\_0 (TMRWp2ak4xmFUztQ7kFnqWPhZ7KJUxJAGkT)}
\maketitle
Let $ v1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_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 $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k1\_funct\_1}~{({{{k16\_funcop\_1}~{X0}}~{X1}})}}~{X0}}={X1}}}}\label{hyp:ehhdcdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}(l1\_memstr\_0~X1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(k4\_struct\_0~X1 \in k9\_xtuple\_0~(k7\_memstr\_0~\\
X0~X1~X2))))\end{array}
\label{hyp:ehbdfdpfngfgngdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
(k1\_funct\_4~X2~X1)~X0=k1\_funct\_1~X1~X0)))\end{array}
\label{hyp:ehbdddpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}\\
(v1\_funct\_1~X2)))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_4~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~\\
(k1\_funct\_4~X1~X2)~X0){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_4~X1~X2))))\end{array}
\label{hyp:ggdghdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~\\
X0)){\unicdcdcdhd}(((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v5\_funct\_1~X1~X0))){\unicdcdcdhd}\\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v5\_funct\_1~X2~X0))))){\unicdbdjdcd}((\\
v1\_relat\_1~(k1\_funct\_4~X1~X2)){\unicdcdcdhd}((v1\_funct\_1~(k1\_funct\_4~X1~X2)){\unicdcdcdhd}\\
(v5\_funct\_1~(k1\_funct\_4~X1~X2)~X0)))\end{array}
\label{hyp:ggdgbdbdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_setfam\_1~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}(l1\_memstr\_0~X1~\\
X0)))){\unicdcdcdhd}(v7\_ordinal1~X2))){\unicdbdjdcd}((v1\_relat\_1~(k7\_memstr\_0~X0~X1~X2)){\unicdcdcdhd}\\
((v4\_relat\_1~(k7\_memstr\_0~X0~X1~X2)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~\\
(k7\_memstr\_0~X0~X1~X2)){\unicdcdcdhd}(v5\_funct\_1~(k7\_memstr\_0~X0~X1~X2)~(k2\_memstr\_0~\\
X0~X1)))))\end{array}
\label{hyp:egehpflghdpfngfgngdhehchpfad}
\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 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdcdcdhd}((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_4~X0~\\
X1)){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_4~X0~X1)))\end{array}
\label{hyp:egehpflgbdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_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))))){\unicdbdjdcd}(k5\_memstr\_0~\\
X0~X1~X2=k1\_funct\_1~X2~(k4\_struct\_0~X1))))\end{array}
\label{hyp:eghdpfngfgngdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}(l1\_memstr\_0~X1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(k7\_memstr\_0~X0~X1~X2=k16\_funcop\_1~\\
(k4\_struct\_0~X1)~X2)))\end{array}
\label{hyp:egbdadpfngfgngdhehchpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfngfgngdhehchpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}(l1\_memstr\_0~X1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~X1)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}(v5\_funct\_1~X2~(k2\_memstr\_0~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(v7\_ordinal1~X3){\unicdbdjdcd}(k5\_memstr\_0~X0~X1~(k1\_funct\_4~X2~(k7\_memstr\_0~\\
X0~X1~X3))=X3))))\end{array}$$
\end{theorem}
\end{document}
