\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{t1\_amistd\_4 (TMPZ2xwQk5e6Q23NUocvNm6t5dgtanG8zSY)}
\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 $ v3\_amistd\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ 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 $ k4\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v4\_amistd\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_amistd\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_ordinal1 : {{\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}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  (X2{\unicdcdgdad}X3){\unicdbdjdcd}(k1\_funct\_1~(k2\_funct\_7~X0~X2~X1)~X3=k1\_funct\_1~\\
X0~X3))\end{array}
\label{hyp:ehddcdpfggfhogdgehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\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\_extpro\_1~X1~X0)))){\unicdcdcdhd}(((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\_partfun1~X2~(u1\_struct\_0~X1)))))){\unicdcdcdhd}((m1\_subset\_1~\\
X3~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X4~(k4\_memstr\_0~X0~X1~X3)))))){\unicdbdjdcd}\\
(k1\_amistd\_4~X0~X1~X2~X3~X4=k2\_funct\_7~X2~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfbgngjgdhehegpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_extpro\_1~X1~X0){\unicdbdjdcd}((l1\_memstr\_0~X1~X0){\unicdcdcdhd}\\
(l1\_compos\_1~X1))\end{array}
\label{hyp:egehpfmgbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_setfam\_1~X0){\unicdcdcdhd}\\
(((v2\_memstr\_0~X1~X0){\unicdcdcdhd}(l1\_extpro\_1~X1~X0)){\unicdcdcdhd}((m1\_subset\_1~X2~(\\
u1\_compos\_1~X1)){\unicdcdcdhd}((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}((v1\_relat\_1~(k2\_extpro\_1~\\
X0~X1~X2~X3)){\unicdcdcdhd}((v4\_relat\_1~(k2\_extpro\_1~X0~X1~X2~X3)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}((v1\_funct\_1~(k2\_extpro\_1~X0~X1~X2~X3)){\unicdcdcdhd}((v5\_funct\_1~(k2\_extpro\_1~\\
X0~X1~X2~X3)~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}(v1\_partfun1~(k2\_extpro\_1~X0~X1~\\
X2~X3)~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:egehpflgcdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\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\_extpro\_1~X1~X0)))){\unicdcdcdhd}(((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\_partfun1~X2~(u1\_struct\_0~X1)))))){\unicdcdcdhd}((m1\_subset\_1~\\
X3~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X4~(k4\_memstr\_0~X0~X1~X3)))))){\unicdbdjdcd}\\
((v1\_relat\_1~(k1\_amistd\_4~X0~X1~X2~X3~X4)){\unicdcdcdhd}((v4\_relat\_1~(k1\_amistd\_4~\\
X0~X1~X2~X3~X4)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k1\_amistd\_4~X0~X1~\\
X2~X3~X4)){\unicdcdcdhd}((v5\_funct\_1~(k1\_amistd\_4~X0~X1~X2~X3~X4)~(k2\_memstr\_0~\\
X0~X1)){\unicdcdcdhd}(v1\_partfun1~(k1\_amistd\_4~X0~X1~X2~X3~X4)~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:egehpflgbdpfbgngjgdhehegpfed}
\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\_extpro\_1~X1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_compos\_1~X1)){\unicdbdjdcd}((v4\_amistd\_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}(k1\_funct\_1~(k2\_extpro\_1~\\
X0~X1~X2~X3)~(k4\_struct\_0~X1)=k1\_ordinal1~(k5\_memstr\_0~X0~X1~X3))))))\end{array}
\label{hyp:egidpfbgngjgdhehegpfbd}
\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}
\begin{theorem}\label{thm:ehbdpfbgngjgdhehegpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_amistd\_1~X1~X0){\unicdcdcdhd}\\
(l1\_extpro\_1~X1~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_compos\_1~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_funct\_1~X3~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}(\\
v1\_partfun1~X3~(u1\_struct\_0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k4\_memstr\_0~\\
X0~X1~X4)){\unicdbdjdcd}((v4\_amistd\_1~X2~X0~X1){\unicdbdjdcd}((X4=k4\_struct\_0~X1){\unicdcdcdid}(k5\_memstr\_0~\\
X0~X1~(k2\_extpro\_1~X0~X1~X2~X3)=k5\_memstr\_0~X0~X1~(k2\_extpro\_1~X0~\\
X1~X2~(k1\_amistd\_4~X0~X1~X3~X4~X5))))))))))\end{array}$$
\end{theorem}
\end{document}
