\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{l19\_xreal\_0 (TMQK983ZPNn9kkBusYK9Vsi8jgoqizEBSfa)}
\maketitle
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_arytm\_2 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_arytm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_arytm\_3 : {\iota}$ be given.
Let $ k12\_arytm\_3 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_arytm\_3 : {\iota}$ be given.
Let $ c5\_\_xreal\_0 : {\iota}$ be given.
Let $ k1\_arytm\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ c3\_\_xreal\_0 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_arytm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}((k7\_arytm\_2~X0~X1=k11\_arytm\_3){\unicdbdjdcd}(X0=k11\_arytm\_3)))\end{array}
\label{hyp:ehfdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{({{k11\_arytm\_3} \in {k2\_arytm\_2}})}{\unicdcdcdhd}{({{k12\_arytm\_3} \in {k2\_arytm\_2}})}}\label{hyp:ehcdadpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k12\_arytm\_3}={k1\_arytm\_3}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k11\_arytm\_3}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(c5\_\_xreal\_0=k4\_xcmplx\_0~np\_\_1){\unicdcdcdhd}(k1\_arytm\_0~c3\_\_xreal\_0~c5\_\_xreal\_0=\\
k6\_numbers)\end{array}
\label{hyp:mgbdidpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{c3\_\_xreal\_0}={np\_\_1}}\label{hyp:mgbdhdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k1\_numbers)){\unicdbdjdcd}(m1\_subset\_1~(k1\_arytm\_0~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v1\_xboole\_0~k12\_arytm\_3){\unicdcdcdhd}((v3\_ordinal1~k12\_arytm\_3){\unicdcdcdhd}(m1\_subset\_1~\\
k12\_arytm\_3~k5\_arytm\_3))\end{array}
\label{hyp:egehpflgbdcdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{c5\_\_xreal\_0}}~{k1\_numbers}}\label{hyp:egehpfdgfdpfpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{c3\_\_xreal\_0}}~{k1\_numbers}}\label{hyp:egehpfdgddpfpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_arytm\_3}={np\_\_1}}\label{hyp:egbdpfbgchjhehngpfdd}
\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~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}((((\\
X0 \in k2\_arytm\_2){\unicdcdcdhd}(X1 \in k2\_arytm\_2)){\unicdbdjdcd}((X2=k1\_arytm\_0~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~k2\_arytm\_2){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~k2\_arytm\_2){\unicdcdcdhd}\\
((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}(X2=k7\_arytm\_2~X3~X4))))))){\unicdcdcdhd}((((X0 \in k2\_arytm\_2){\unicdcdcdhd}\\
(X1 \in k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~k2\_arytm\_2)){\unicdbdjdcd}((X2=k1\_arytm\_0~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k2\_arytm\_2){\unicdcdcdhd}({\unicdcdaddd} X4 .  (\\
m1\_subset\_1~X4~k2\_arytm\_2){\unicdcdcdhd}((X0=X3){\unicdcdcdhd}((X1=k4\_tarski~k6\_numbers~\\
X4){\unicdcdcdhd}(X2=k2\_arytm\_1~X3~X4))))))){\unicdcdcdhd}((((X1 \in k2\_arytm\_2){\unicdcdcdhd}(X0 \in k2\_zfmisc\_1~\\
(k1\_tarski~k6\_numbers)~k2\_arytm\_2)){\unicdbdjdcd}((X2=k1\_arytm\_0~X0~X1){\unicdbdjded}\\
({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k2\_arytm\_2){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~k2\_arytm\_2){\unicdcdcdhd}((X0=k4\_tarski~k6\_numbers~X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}(X2=\\
k2\_arytm\_1~X4~X3))))))){\unicdcdcdhd}(\preoh (\preoh (X0 \in k2\_arytm\_2){\unicdcdcdhd}(X1 \in k2\_arytm\_2)){\unicdcdcdhd}\\
((\preoh (X0 \in k2\_arytm\_2){\unicdcdcdhd}(X1 \in k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~\\
k2\_arytm\_2)){\unicdcdcdhd}((\preoh (X1 \in k2\_arytm\_2){\unicdcdcdhd}(X0 \in k2\_zfmisc\_1~(k1\_tarski~\\
k6\_numbers)~k2\_arytm\_2)){\unicdcdcdhd}(\preoh (X2=k1\_arytm\_0~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~k2\_arytm\_2){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~k2\_arytm\_2){\unicdcdcdhd}\\
((X0=k4\_tarski~k6\_numbers~X3){\unicdcdcdhd}((X1=k4\_tarski~k6\_numbers~X4){\unicdcdcdhd}\\
(X2=k4\_tarski~k6\_numbers~(k7\_arytm\_2~X3~X4)))))))))))))))\end{array}
\label{hyp:egbdpfbgchjhehngpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdjdpfihchfgbgmgpfad}
${\preoh{{{{k4\_xcmplx\_0}~{np\_\_1}} \in {k2\_arytm\_2}}}}$.
\end{theorem}
\end{document}
