\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{t37\_rat\_1 (TMc7K3AHy4HkA1KZQbsEhSH91p8FnYrkvny)}
\maketitle
Let $ v1\_rat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_rat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_rat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k6\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}((X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k7\_xcmplx\_0~\\
X0~X0=np\_\_1))\end{array}
\label{hyp:ehgdadpfihdgngahmgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k3\_xcmplx\_0}~{np\_\_1}}~{X0}}={X0}})}}}\label{hyp:ehddpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{r1\_xxreal\_0}~{k6\_numbers}}~{X0}})}}}\label{hyp:ehcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_rat\_1~X0){\unicdbdjdcd}(((k2\_rat\_1~X0=X0){\unicdcdcdid}(k1\_rat\_1~X0=np\_\_1)){\unicdbdjdcd}\\
(v1\_int\_1~X0))\end{array}
\label{hyp:ehbdidpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_rat\_1~X0){\unicdbdjdcd}((v1\_int\_1~X0){\unicdbdjdcd}((k1\_rat\_1~X0=np\_\_1){\unicdcdcdhd}\\
(k2\_rat\_1~X0=X0)))\end{array}
\label{hyp:ehbdhdpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_rat\_1~X0){\unicdbdjdcd}((X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k1\_rat\_1~X0=k7\_xcmplx\_0~\\
(k2\_rat\_1~X0)~X0))\end{array}
\label{hyp:ehbdgdpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_rat\_1~X0){\unicdbdjdcd}((k2\_rat\_1~X0=k6\_numbers){\unicdbdjded}(X0=k6\_numbers))\end{array}
\label{hyp:ehbdedpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(\preoh (\preoh \\
r1\_xxreal\_0~(k7\_xcmplx\_0~X0~X1)~k6\_numbers){\unicdcdcdhd}((\preoh (\preoh r1\_xxreal\_0~\\
X1~k6\_numbers){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X0~k6\_numbers)){\unicdcdcdhd}(\preoh (\preoh r1\_xxreal\_0~\\
k6\_numbers~X1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~k6\_numbers~X0)))))\end{array}
\label{hyp:ehbdededpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(\preoh (\preoh \\
r1\_xxreal\_0~k6\_numbers~X0){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X1~k6\_numbers){\unicdcdcdhd}(r1\_xxreal\_0~\\
k6\_numbers~(k7\_xcmplx\_0~X0~X1)))))\end{array}
\label{hyp:ehbdedbdpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X0~k6\_numbers){\unicdcdcdhd}(r1\_xxreal\_0~k6\_numbers~X0)){\unicdbdjdcd}(k6\_numbers=k3\_xcmplx\_0~\\
X0~X1)))\end{array}
\label{hyp:ehbdcdgdpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_rat\_1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{{r1\_xxreal\_0}~{({{k1\_rat\_1}~{X0}})}}~{k6\_numbers}}}})}}}\label{hyp:ehbdadpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_rat\_1~X0){\unicdcdcdhd}(v1\_rat\_1~X1)){\unicdbdjdcd}(v1\_rat\_1~\\
(k7\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgedpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_rat\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_int\_1}~{({{k2\_rat\_1}~{X0}})}})}}}\label{hyp:egehpflgcdpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_rat\_1~X0){\unicdbdjdcd}(m2\_subset\_1~(k1\_rat\_1~X0)~k1\_numbers~\\
k5\_numbers)\end{array}
\label{hyp:egehpflgbdpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_rat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}((X1=k1\_rat\_1~X0){\unicdbdjded}((X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(({\unicdcdaddd} X2 .  \\
(v1\_int\_1~X2){\unicdcdcdhd}(X0=k6\_real\_1~X2~X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}((X0=k6\_real\_1~\\
X2~X3){\unicdbdjdcd}((X3=k6\_numbers){\unicdcdcdid}(r1\_xxreal\_0~X1~X3)))))))))\end{array}
\label{hyp:egddpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgddpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_rat\_1}~{X0}})}}}\label{hyp:dgdgcdpfchbgehpfbd}
\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}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_rat\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfchbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfchbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_rat\_1~X0){\unicdbdjdcd}((\preoh (\preoh r1\_xxreal\_0~k6\_numbers~X0){\unicdcdcdhd}(r1\_xxreal\_0~\\
k6\_numbers~(k2\_rat\_1~X0))){\unicdcdcdhd}(\preoh (\preoh r1\_xxreal\_0~k6\_numbers~(k2\_rat\_1~\\
X0)){\unicdcdcdhd}(r1\_xxreal\_0~k6\_numbers~X0)))\end{array}$$
\end{theorem}
\end{document}
