\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{t43\_real\_3 (TMV2f8aGrbtpF4RDUCmpRJyNxNATAu83UBa)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_real\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_rat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_power : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v1\_rat\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (v7\_ordinal1~\\
X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((r1\_xxreal\_0~X1~X2){\unicdbdjdcd}(k1\_seq\_1~\\
(k4\_real\_3~X0)~X2=k6\_numbers)))))\end{array}
\label{hyp:ehedcdpfchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (v1\_xreal\_0~X0){\unicdcdcdhd}({\unicdcdaddd} X1 .  (v1\_xreal\_0~X1){\unicdcdcdhd}((\preoh v1\_rat\_1~\\
X0){\unicdcdcdhd}((\preoh v1\_rat\_1~X1){\unicdcdcdhd}(v1\_rat\_1~(k3\_power~X0~X1)))))\end{array}
\label{hyp:ehcdpfjgchchbgehpfbd}
\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:ehedddpfchfgbgmgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(\preoh ({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\\
k1\_seq\_1~(k4\_real\_3~X0)~X1{\unicdcdgdad}k6\_numbers)){\unicdcdcdhd}(v1\_rat\_1~X0))\end{array}$$
\end{theorem}
\end{document}
