\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{t127\_tmap\_1 (TMYTtfsTJ7ECs8qGrRxFySo4rdgSAktNCxG)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_tsep\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k10\_tmap\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_tmap\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_tmap\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(m1\_pre\_topc~X2~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X2)~\\
(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X2)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}(r2\_funct\_2~(u1\_struct\_0~\\
X2)~(u1\_struct\_0~X1)~X3~(k3\_tmap\_1~X0~X1~X2~X2~X3)))))\end{array}
\label{hyp:ehgdhdpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(m1\_pre\_topc~X2~X1)){\unicdbdjdcd}(\\
{\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X2)~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X2)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}({\unicdcdaddd} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)))))){\unicdcdcdhd}\\
(r2\_funct\_2~(u1\_struct\_0~X2)~(u1\_struct\_0~X0)~(k2\_tmap\_1~X1~X0~\\
X4~X2)~X3)))))\end{array}
\label{hyp:ehfdhdpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{{m1\_pre\_topc}~{X0}}~{X0}})}}}\label{hyp:ehcdpfehdhfgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(m1\_pre\_topc~X2~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}(m1\_pre\_topc~X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~(k1\_tsep\_1~X0~X2~\\
X3))~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_tsep\_1~X0~X2~X3))~(u1\_struct\_0~X1)))))){\unicdbdjdcd}(r2\_funct\_2~\\
(u1\_struct\_0~(k1\_tsep\_1~X0~X2~X3))~(u1\_struct\_0~X1)~X4~(k10\_tmap\_1~\\
X0~X1~X2~X3~(k3\_tmap\_1~X0~X1~(k1\_tsep\_1~X0~X2~X3)~X2~X4)~(k3\_tmap\_1~X0~\\
X1~(k1\_tsep\_1~X0~X2~X3)~X3~X4)))))))\end{array}
\label{hyp:ehbdcdgdpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~\\
X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}((\\
v1\_funct\_2~X4~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))))))){\unicdbdjdcd}((r1\_funct\_2~X0~X1~\\
X2~X3~X4~X5){\unicdbdjded}(X4=X5))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfggfhogdgehpfcd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_pre\_topc~X1~X0){\unicdbdjdcd}\\
(l1\_pre\_topc~X1))\end{array}
\label{hyp:egehpfngbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdcdcdhd}((m1\_pre\_topc~X2~X0){\unicdcdcdhd}(\\
(m1\_pre\_topc~X3~X0){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~\\
X2)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X2)~(u1\_struct\_0~X1)))))))))){\unicdbdjdcd}((v1\_funct\_1~(k3\_tmap\_1~\\
X0~X1~X2~X3~X4)){\unicdcdcdhd}((v1\_funct\_2~(k3\_tmap\_1~X0~X1~X2~X3~X4)~(u1\_struct\_0~\\
X3)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k3\_tmap\_1~X0~X1~X2~X3~X4)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X3)~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:egehpflgddpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((l1\_struct\_0~X0){\unicdcdcdhd}\\
((l1\_struct\_0~X1){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdcdcdhd}(l1\_struct\_0~X3)))){\unicdbdjdcd}\\
((v1\_funct\_1~(k2\_tmap\_1~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k2\_tmap\_1~\\
X0~X1~X2~X3)~(u1\_struct\_0~X3)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k2\_tmap\_1~\\
X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X3)~(u1\_struct\_0~\\
X1))))))\end{array}
\label{hyp:egehpflgcdpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0))){\unicdcdcdhd}(\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdcdcdhd}((\\
(\preoh v2\_struct\_0~X2){\unicdcdcdhd}(m1\_pre\_topc~X2~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X3){\unicdcdcdhd}\\
(m1\_pre\_topc~X3~X0)){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~\\
X2)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X2)~(u1\_struct\_0~X1)))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~\\
X5~(u1\_struct\_0~X3)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X3)~(u1\_struct\_0~X1))))))))))){\unicdbdjdcd}((\\
v1\_funct\_1~(k10\_tmap\_1~X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}((v1\_funct\_2~(k10\_tmap\_1~\\
X0~X1~X2~X3~X4~X5)~(u1\_struct\_0~(k1\_tsep\_1~X0~X2~X3))~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~(k10\_tmap\_1~X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_tsep\_1~X0~X2~X3))~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:egehpflgbdadpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_pre\_topc~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_pre\_topc~\\
X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~\\
X2)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X2)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((m1\_pre\_topc~X3~X2){\unicdbdjdcd}\\
(k3\_tmap\_1~X0~X1~X2~X3~X4=k2\_partfun1~(u1\_struct\_0~X2)~(u1\_struct\_0~\\
X1)~X4~(u1\_struct\_0~X3)))))))\end{array}
\label{hyp:egfdpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_pre\_topc~\\
X3~X0){\unicdbdjdcd}(k2\_tmap\_1~X0~X1~X2~X3=k2\_partfun1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~X2~(u1\_struct\_0~X3)))))\end{array}
\label{hyp:egedpfehngbgahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdhdpfehngbgahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(m1\_pre\_topc~X2~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}(m1\_pre\_topc~X3~X0)){\unicdbdjdcd}((X0=k1\_tsep\_1~\\
X0~X2~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}(r1\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~(k1\_tsep\_1~X0~X2~X3))~(u1\_struct\_0~\\
X1)~X4~(k10\_tmap\_1~X0~X1~X2~X3~(k2\_tmap\_1~X0~X1~X4~X2)~(k2\_tmap\_1~X0~\\
X1~X4~X3))))))))\end{array}$$
\end{theorem}
\end{document}
