\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{t28\_real\_3 (TMHx7RgLYzDLpNgkBFPJeSFLSU1cyg95wkx)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_real\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_real\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_int\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  \preoh (v1\_xboole\_0~X0){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdcdcdhd}(v1\_xboole\_0~\\
X1))\end{array}
\label{hyp:ehidpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(((k1\_seq\_1~(k3\_real\_3~X2)~X0=k6\_numbers){\unicdcdcdhd}(\\
r1\_xxreal\_0~X0~X1)){\unicdbdjdcd}(k1\_seq\_1~(k3\_real\_3~X2)~X1=k6\_numbers))))\end{array}
\label{hyp:ehcdhdpfchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_xboole\_0}~{({{k1\_int\_1}~{k6\_numbers}})}})}{\unicdcdcdhd}{({{v1\_int\_1}~{({{k1\_int\_1}~{k6\_numbers}})}})}}\label{hyp:ggdghdpfchfgbgmgpfdd}
\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 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v5\_relat\_1~(k4\_real\_3~X0)~k4\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~(k4\_real\_3~X0)){\unicdcdcdhd}((v1\_funct\_2~(k4\_real\_3~X0)~k5\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k4\_real\_3~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers))))))\end{array}
\label{hyp:egehpflgedpfchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v5\_relat\_1~X1~k4\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))){\unicdbdjdcd}((\\
X1=k4\_real\_3~X0){\unicdbdjded}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(k1\_seq\_1~X1~X2=\\
k1\_int\_1~(k1\_seq\_1~(k3\_real\_3~X0)~X2)))))\end{array}
\label{hyp:egedpfchfgbgmgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfchfgbgmgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(((k1\_seq\_1~(k3\_real\_3~X2)~X0=k6\_numbers){\unicdcdcdhd}(\\
r1\_xxreal\_0~X0~X1)){\unicdbdjdcd}(k1\_seq\_1~(k4\_real\_3~X2)~X1=k6\_numbers))))\end{array}$$
\end{theorem}
\end{document}
