\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=}
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\newcommand\unicdcdcdjd{\cap}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t45\_int\_1 (TMLVyskJ1shMCP43Yb1NneVjCtkEApMXQdp)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_int\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_int\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_int\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{{k1\_int\_1}~{({{k4\_int\_1}~{X0}})}}={k6\_numbers}})}}}\label{hyp:ehededpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((\preoh r1\_xxreal\_0~np\_\_1~(k4\_int\_1~X0)){\unicdcdcdhd}\\
(r1\_xxreal\_0~k6\_numbers~(k4\_int\_1~X0)))\end{array}
\label{hyp:ehedddpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((\preoh (\preoh r1\_xxreal\_0~X0~(k1\_int\_1~X0)){\unicdcdcdhd}\\
(v1\_int\_1~X0)){\unicdcdcdhd}(\preoh (\preoh v1\_int\_1~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~(k1\_int\_1~X0))))\end{array}
\label{hyp:ehcdgdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{({{{k1\_int\_1}~{X0}}={X0}})}{\unicdbdjded}{({{v1\_int\_1}~{X0}})}})}}}\label{hyp:ehcdfdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{{k4\_int\_1}~{X0}}={{k3\_int\_1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfjgogehpfbd}
\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~X1~X0){\unicdcdcdhd}(r1\_xxreal\_0~(k6\_xcmplx\_0~X1~X0)~k6\_numbers)))\end{array}
\label{hyp:mgedgdpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k3\_int\_1}~{X0}})}})}}}\label{hyp:ggdgfdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v1\_int\_1~\\
(k6\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgedpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_int\_1}~{({{k1\_int\_1}~{X0}})}})}}}\label{hyp:egehpflgbdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{{k3\_int\_1}~{X0}}={{{k6\_xcmplx\_0}~{X0}}~{({{k1\_int\_1}~{X0}})}}})}}}\label{hyp:egidpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgddpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfjgogehpfbd}
${{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{({{{k4\_int\_1}~{X0}}={k6\_numbers}})}{\unicdbdjded}{({{v1\_int\_1}~{X0}})}})}}}$.
\end{theorem}
\end{document}
