\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{l22\_prepower (TMVKPCKTPuTTPm2zvGFcU8kgp2MKo8DMgFj)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_newton : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_prepower : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh (\\
\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_newton~X0~X1)~k6\_numbers)))\end{array}
\label{hyp:ehgdpfahchfgahpghhfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(v1\_xreal\_0~\\
(k1\_newton~X0~X1))\end{array}
\label{hyp:ggdgcdpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(v1\_xreal\_0~\\
(k2\_prepower~X0~X1))\end{array}
\label{hyp:egehpflgcdpfahchfgahpghhfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
np\_\_1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(((\preoh r1\_xxreal\_0~X1~k6\_numbers){\unicdbdjdcd}\\
((X2=k2\_prepower~X0~X1){\unicdbdjded}((k1\_newton~X2~X0=X1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~\\
X2~k6\_numbers)))){\unicdcdcdhd}((X1=k6\_numbers){\unicdbdjdcd}((X2=k2\_prepower~X0~X1){\unicdbdjded}\\
(X2=k6\_numbers)))))))\end{array}
\label{hyp:egcdpfahchfgahpghhfgch}
\end{equation}
\begin{theorem}\label{thm:mgcdcdpfahchfgahpghhfgch}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
np\_\_1~X1){\unicdbdjdcd}((r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdid}((k1\_newton~(k2\_prepower~\\
X1~X0)~X1=X0){\unicdcdcdhd}(k2\_prepower~X1~(k1\_newton~X0~X1)=X0)))))\end{array}$$
\end{theorem}
\end{document}
