\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{t63\_jgraph\_7 (TMbk5RWWZrWHBk6E3ShFkmL8ZHBCa76vgcP)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\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 $ k5\_topmetr : {\iota}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_jgraph\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))))))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))))))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~k5\_topmetr)){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~k5\_topmetr)){\unicdbdjdcd}(((r2\_funct\_2~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X4~(k2\_jgraph\_2~(k10\_real\_1~np\_\_2~(k6\_xcmplx\_0~X1~X0))~(k4\_xcmplx\_0~\\
(k7\_xcmplx\_0~(k2\_xcmplx\_0~X1~X0)~(k6\_xcmplx\_0~X1~X0)))~(k10\_real\_1~\\
np\_\_2~(k6\_xcmplx\_0~X3~X2))~(k4\_xcmplx\_0~(k7\_xcmplx\_0~(k2\_xcmplx\_0~\\
X3~X2)~(k6\_xcmplx\_0~X3~X2))))){\unicdcdcdhd}((r1\_xxreal\_0~X2~(k18\_euclid~(k3\_funct\_2~\\
(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X5~\\
X6))){\unicdcdcdhd}((r1\_xxreal\_0~(k18\_euclid~(k3\_funct\_2~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X5~X6))~X3){\unicdcdcdhd}((r1\_xxreal\_0~X0~\\
(k17\_euclid~(k3\_funct\_2~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X5~X7))){\unicdcdcdhd}(r1\_xxreal\_0~(k17\_euclid~(k3\_funct\_2~\\
(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X5~\\
X7))~X1))))){\unicdbdjdcd}((r1\_xxreal\_0~X1~X0){\unicdcdcdid}((r1\_xxreal\_0~X3~X2){\unicdcdcdid}((r1\_xxreal\_0~\\
(k1\_real\_1~np\_\_1)~(k18\_euclid~(k3\_funct\_2~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_partfun1~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X5~X4)~X6))){\unicdcdcdhd}((r1\_xxreal\_0~(\\
k18\_euclid~(k3\_funct\_2~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k1\_partfun1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X5~X4)~X6))~np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_real\_1~\\
np\_\_1)~(k17\_euclid~(k3\_funct\_2~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k1\_partfun1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X5~X4)~X7))){\unicdcdcdhd}(r1\_xxreal\_0~(k17\_euclid~(k3\_funct\_2~\\
(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_partfun1~\\
(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X5~X4)~X7))~\\
np\_\_1))))))))))))))\end{array}
\label{hyp:ehfdjdpfkghgchbgahigpfhd}
\end{equation}
\begin{theorem}\label{thm:ehgdddpfkghgchbgahigpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))))))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))))))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~k5\_topmetr)){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~k5\_topmetr)){\unicdbdjdcd}(((r2\_funct\_2~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X4~(k2\_jgraph\_2~(k10\_real\_1~np\_\_2~(k6\_xcmplx\_0~X1~X0))~(k4\_xcmplx\_0~\\
(k7\_xcmplx\_0~(k2\_xcmplx\_0~X1~X0)~(k6\_xcmplx\_0~X1~X0)))~(k10\_real\_1~\\
np\_\_2~(k6\_xcmplx\_0~X3~X2))~(k4\_xcmplx\_0~(k7\_xcmplx\_0~(k2\_xcmplx\_0~\\
X3~X2)~(k6\_xcmplx\_0~X3~X2))))){\unicdcdcdhd}((r1\_xxreal\_0~X0~(k17\_euclid~(k3\_funct\_2~\\
(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X5~\\
X6))){\unicdcdcdhd}((r1\_xxreal\_0~(k17\_euclid~(k3\_funct\_2~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X5~X6))~X1){\unicdcdcdhd}((r1\_xxreal\_0~X2~\\
(k18\_euclid~(k3\_funct\_2~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X5~X7))){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~(k3\_funct\_2~\\
(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X5~\\
X7))~X3))))){\unicdbdjdcd}((r1\_xxreal\_0~X1~X0){\unicdcdcdid}((r1\_xxreal\_0~X3~X2){\unicdcdcdid}((r1\_xxreal\_0~\\
(k1\_real\_1~np\_\_1)~(k17\_euclid~(k3\_funct\_2~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_partfun1~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X5~X4)~X6))){\unicdcdcdhd}((r1\_xxreal\_0~(\\
k17\_euclid~(k3\_funct\_2~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k1\_partfun1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X5~X4)~X6))~np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_real\_1~\\
np\_\_1)~(k18\_euclid~(k3\_funct\_2~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k1\_partfun1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X5~X4)~X7))){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~(k3\_funct\_2~\\
(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_partfun1~\\
(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X5~X4)~X7))~\\
np\_\_1))))))))))))))\end{array}$$
\end{theorem}
\end{document}
