\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{t4\_amistd\_4 (TMLcy4ZL552bFjv2YoYv5znjQtQngP2x3Ud)}
\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\_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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_amistd\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_amistd\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_relset\_1 : {{\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 $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
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}(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\_partfun1~X2~(u1\_struct\_0~X1)))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}(k1\_funct\_1~X2~\\
X3 \in k4\_memstr\_0~X0~X1~X3))))\end{array}
\label{hyp:ehhdhdpfngfgngdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  k2\_funct\_7~\\
X0~X1~(k1\_funct\_1~X0~X1)=X0)\end{array}
\label{hyp:ehddfdpfggfhogdgehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
(X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}(k1\_funct\_1~(k2\_funct\_7~X0~X2~X1)~X2=X1))\end{array}
\label{hyp:ehddbdpfggfhogdgehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~X0){\unicdbdjdcd}((X3 \in X1){\unicdbdjdcd}(X3 \in X2))){\unicdbdjdcd}(r1\_tarski~X1~X2)))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
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}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k1\_relset\_1~X0~X1=k9\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgmgdhfgehpfbd}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{l1\_memstr\_0}~{X1}}~{X0}})}{\unicdbdjdcd}{({{l2\_struct\_0}~{X1}})}}}}\label{hyp:egehpfmgbdpfngfgngdhehchpfad}
\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 .  ((\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}(m1\_subset\_1~X2~(u1\_compos\_1~X1)))){\unicdbdjdcd}(m1\_subset\_1~(k4\_amistd\_4~\\
X0~X1~X2)~(k1\_zfmisc\_1~(u1\_struct\_0~X1)))\end{array}
\label{hyp:egehpflgedpfbgngjgdhehegpfed}
\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 .  ((\preoh v1\_setfam\_1~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_memstr\_0~X1~X0){\unicdcdcdhd}(l1\_extpro\_1~X1~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_compos\_1~X1)))){\unicdbdjdcd}(m1\_subset\_1~(k2\_amistd\_4~X0~X1~X2)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1)))\end{array}
\label{hyp:egehpflgcdpfbgngjgdhehegpfed}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}((X3=k4\_amistd\_4~X0~X1~X2){\unicdbdjded}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdbdjdcd}((X4 \in X3){\unicdbdjded}(\preoh {\unicdcdadad} X5 .  \\
((v1\_relat\_1~X5){\unicdcdcdhd}((v4\_relat\_1~X5~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v5\_funct\_1~X5~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}(v1\_partfun1~X5~(u1\_struct\_0~\\
X1)))))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k4\_memstr\_0~X0~X1~X4)){\unicdbdjdcd}\\
(k2\_extpro\_1~X0~X1~X2~(k1\_amistd\_4~X0~X1~X5~X4~X6)=k1\_amistd\_4~X0~\\
X1~(k2\_extpro\_1~X0~X1~X2~X5)~X4~X6)))))))))\end{array}
\label{hyp:egfdpfbgngjgdhehegpfed}
\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}(l1\_extpro\_1~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_compos\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1))){\unicdbdjdcd}((X3=k2\_amistd\_4~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X1)){\unicdbdjdcd}((X4 \in X3){\unicdbdjded}(\preoh {\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}\\
((v4\_relat\_1~X5~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v5\_funct\_1~\\
X5~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}(v1\_partfun1~X5~(u1\_struct\_0~X1)))))){\unicdbdjdcd}\\
(k1\_funct\_1~X5~X4=k1\_funct\_1~(k2\_extpro\_1~X0~X1~X2~X5)~X4))))))))\end{array}
\label{hyp:egddpfbgngjgdhehegpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
(v1\_partfun1~X1~X0){\unicdbdjded}(k1\_relset\_1~X0~X1=X0))\end{array}
\label{hyp:egcdpfahbgchehggfhogbd}
\end{equation}
\begin{theorem}\label{thm:ehedpfbgngjgdhehegpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}(l1\_extpro\_1~X1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_compos\_1~X1)){\unicdbdjdcd}(r1\_tarski~(k2\_amistd\_4~\\
X0~X1~X2)~(k4\_amistd\_4~X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
