\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{t57\_jgraph\_5 (TMK6ynsdwLkwJJZeLgSKVkXkRKZmHQJBCxz)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ 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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_jgraph\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k13\_complex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X0~(k1\_real\_1~\\
np\_\_1)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}((\preoh r1\_xxreal\_0~k6\_numbers~\\
(k18\_euclid~X1)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdcdcdhd}((X2=k3\_funct\_2~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))~(k9\_jgraph\_4~X0)~X1){\unicdcdcdhd}(r1\_xxreal\_0~\\
k6\_numbers~(k18\_euclid~X2))))))))\end{array}
\label{hyp:ehcdfdpfkghgchbgahigpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(((r1\_xxreal\_0~X1~(k13\_complex1~\\
(k17\_euclid~X0)~(k12\_euclid~X0))){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~(\\
k18\_euclid~X0)){\unicdcdcdid}(k3\_funct\_2~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k9\_jgraph\_4~X1)~X0=k19\_euclid~\\
(k8\_real\_1~(k12\_euclid~X0)~(k13\_complex1~(k6\_xcmplx\_0~(k13\_complex1~\\
(k17\_euclid~X0)~(k12\_euclid~X0))~X1)~(k9\_real\_1~np\_\_1~X1)))~(k8\_real\_1~\\
(k12\_euclid~X0)~(k1\_real\_1~(k7\_square\_1~(k9\_real\_1~np\_\_1~(k4\_square\_1~\\
(k13\_complex1~(k6\_xcmplx\_0~(k13\_complex1~(k17\_euclid~X0)~(k12\_euclid~\\
X0))~X1)~(k9\_real\_1~np\_\_1~X1)))))))))){\unicdcdcdhd}((r1\_xxreal\_0~k6\_numbers~\\
(k18\_euclid~X0)){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k9\_jgraph\_4~X1)~X0=X0))))\end{array}
\label{hyp:ehbdbdddpfkghgchbgahigpfed}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xcmplx\_0~X0){\unicdcdcdhd}((v1\_xxreal\_0~\\
X0){\unicdcdcdhd}(v1\_xreal\_0~X0)))\end{array}
\label{hyp:chdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(m1\_subset\_1~(k18\_euclid~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdidpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdhdpfkghgchbgahigpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}((r1\_xxreal\_0~(k18\_euclid~\\
X1)~k6\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~X0~(k1\_real\_1~np\_\_1)){\unicdcdcdid}((r1\_xxreal\_0~\\
np\_\_1~X0){\unicdcdcdid}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}((X2=k3\_funct\_2~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))~(k9\_jgraph\_4~X0)~X1){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k18\_euclid~X2)~k6\_numbers)))))))\end{array}$$
\end{theorem}
\end{document}
