\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{t6\_reloc (TMS5w56Hfv2AZB38Q4ZX1VnFmchJFBMsF1L)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ami\_3 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ np\_\_2 : {\iota}$ be given.
Let $ v4\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k5\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~\\
(u1\_compos\_1~k1\_ami\_3)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}\\
(\preoh v2\_compos\_1~X1~k1\_ami\_3)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~\\
X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~k1\_ami\_3)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_2~k1\_ami\_3)){\unicdcdcdhd}\\
((v1\_finset\_1~X2){\unicdcdcdhd}(v4\_extpro\_1~X2~np\_\_2~k1\_ami\_3~X1))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~(u1\_struct\_0~k1\_ami\_3)){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_funct\_1~X3~(k2\_memstr\_0~np\_\_2~k1\_ami\_3)){\unicdcdcdhd}\\
(v1\_partfun1~X3~(u1\_struct\_0~k1\_ami\_3)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}((v4\_relat\_1~X4~(u1\_struct\_0~k1\_ami\_3)){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}\\
((v5\_funct\_1~X4~(k2\_memstr\_0~np\_\_2~k1\_ami\_3)){\unicdcdcdhd}(v1\_partfun1~X4~\\
(u1\_struct\_0~k1\_ami\_3)))))){\unicdbdjdcd}(((r1\_tarski~X2~X3){\unicdcdcdhd}(r1\_tarski~\\
(k9\_memstr\_0~np\_\_2~k1\_ami\_3~X2~X0)~X4)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~\\
X5){\unicdcdcdhd}((v4\_relat\_1~X5~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X5~(u1\_compos\_1~\\
k1\_ami\_3)){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(v1\_partfun1~X5~k5\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}((v4\_relat\_1~X6~k5\_numbers){\unicdcdcdhd}((\\
v5\_relat\_1~X6~(u1\_compos\_1~k1\_ami\_3)){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}(v1\_partfun1~\\
X6~k5\_numbers))))){\unicdbdjdcd}(((r1\_tarski~X1~X5){\unicdcdcdhd}(r1\_tarski~(k6\_compos\_1~\\
k1\_ami\_3~X1~X0)~X6)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m2\_subset\_1~X7~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
((k2\_nat\_1~(k5\_memstr\_0~np\_\_2~k1\_ami\_3~(k5\_extpro\_1~np\_\_2~k1\_ami\_3~\\
X5~X3~X7))~X0=k5\_memstr\_0~np\_\_2~k1\_ami\_3~(k5\_extpro\_1~np\_\_2~k1\_ami\_3~\\
X6~X4~X7)){\unicdcdcdhd}((k5\_compos\_0~(u1\_compos\_1~k1\_ami\_3)~(k3\_extpro\_1~\\
np\_\_2~k1\_ami\_3~X5~(k5\_extpro\_1~np\_\_2~k1\_ami\_3~X5~X3~X7))~X0=k3\_extpro\_1~\\
np\_\_2~k1\_ami\_3~X6~(k5\_extpro\_1~np\_\_2~k1\_ami\_3~X6~X4~X7)){\unicdcdcdhd}((k5\_relat\_1~\\
(k5\_extpro\_1~np\_\_2~k1\_ami\_3~X5~X3~X7)~(k9\_xtuple\_0~(k6\_memstr\_0~\\
np\_\_2~k1\_ami\_3~X2))=k5\_relat\_1~(k5\_extpro\_1~np\_\_2~k1\_ami\_3~X6~\\
X4~X7)~(k9\_xtuple\_0~(k6\_memstr\_0~np\_\_2~k1\_ami\_3~X2))){\unicdcdcdhd}(k6\_memstr\_0~\\
np\_\_2~k1\_ami\_3~(k5\_extpro\_1~np\_\_2~k1\_ami\_3~X5~(k1\_funct\_4~X3~(k6\_memstr\_0~\\
np\_\_2~k1\_ami\_3~X4))~X7)=k6\_memstr\_0~np\_\_2~k1\_ami\_3~(k5\_extpro\_1~\\
np\_\_2~k1\_ami\_3~X6~X4~X7))))))))))))))\end{array}
\label{hyp:mggdpfchfgmgpgdg}
\end{equation}
\begin{theorem}\label{thm:ehgdpfchfgmgpgdg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~\\
(u1\_compos\_1~k1\_ami\_3)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}\\
(\preoh v2\_compos\_1~X1~k1\_ami\_3)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~\\
X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~k1\_ami\_3)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_2~k1\_ami\_3)){\unicdcdcdhd}\\
((v1\_finset\_1~X2){\unicdcdcdhd}(v4\_extpro\_1~X2~np\_\_2~k1\_ami\_3~X1))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~(u1\_struct\_0~k1\_ami\_3)){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_funct\_1~X3~(k2\_memstr\_0~np\_\_2~k1\_ami\_3)){\unicdcdcdhd}\\
(v1\_partfun1~X3~(u1\_struct\_0~k1\_ami\_3)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}((v4\_relat\_1~X4~(u1\_struct\_0~k1\_ami\_3)){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}\\
((v5\_funct\_1~X4~(k2\_memstr\_0~np\_\_2~k1\_ami\_3)){\unicdcdcdhd}(v1\_partfun1~X4~\\
(u1\_struct\_0~k1\_ami\_3)))))){\unicdbdjdcd}(((k4\_struct\_0~k1\_ami\_3 \in k9\_xtuple\_0~\\
X2){\unicdcdcdhd}((r1\_tarski~X2~X3){\unicdcdcdhd}(r1\_tarski~(k9\_memstr\_0~np\_\_2~k1\_ami\_3~\\
X2~X0)~X4))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}((v4\_relat\_1~X5~k5\_numbers){\unicdcdcdhd}\\
((v5\_relat\_1~X5~(u1\_compos\_1~k1\_ami\_3)){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(v1\_partfun1~\\
X5~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}((v4\_relat\_1~\\
X6~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X6~(u1\_compos\_1~k1\_ami\_3)){\unicdcdcdhd}((v1\_funct\_1~\\
X6){\unicdcdcdhd}(v1\_partfun1~X6~k5\_numbers))))){\unicdbdjdcd}(((r1\_tarski~X1~X5){\unicdcdcdhd}(r1\_tarski~\\
(k6\_compos\_1~k1\_ami\_3~X1~X0)~X6)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m2\_subset\_1~X7~\\
k1\_numbers~k5\_numbers){\unicdbdjdcd}(k2\_nat\_1~(k5\_memstr\_0~np\_\_2~k1\_ami\_3~\\
(k5\_extpro\_1~np\_\_2~k1\_ami\_3~X5~X3~X7))~X0=k5\_memstr\_0~np\_\_2~k1\_ami\_3~\\
(k5\_extpro\_1~np\_\_2~k1\_ami\_3~X6~X4~X7)))))))))))\end{array}$$
\end{theorem}
\end{document}
