\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{l55\_wsierp\_1 (TMNxR4w6PsvkvqrEwhuMGsUYm66jBThJz3o)}
\maketitle
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_int\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(((r1\_int\_1~\\
X0~X1){\unicdbdjdcd}(r1\_int\_1~X0~(k4\_xcmplx\_0~X1))){\unicdcdcdhd}(((r1\_int\_1~X0~(k4\_xcmplx\_0~\\
X1)){\unicdbdjdcd}(r1\_int\_1~X0~X1)){\unicdcdcdhd}(((r1\_int\_1~X0~X1){\unicdbdjdcd}(r1\_int\_1~(k4\_xcmplx\_0~\\
X0)~X1)){\unicdcdcdhd}(((r1\_int\_1~(k4\_xcmplx\_0~X0)~X1){\unicdbdjdcd}(r1\_int\_1~X0~X1)){\unicdcdcdhd}(\\
((r1\_int\_1~X0~X1){\unicdbdjdcd}(r1\_int\_1~(k4\_xcmplx\_0~X0)~(k4\_xcmplx\_0~X1))){\unicdcdcdhd}\\
(((r1\_int\_1~(k4\_xcmplx\_0~X0)~(k4\_xcmplx\_0~X1)){\unicdbdjdcd}(r1\_int\_1~X0~X1)){\unicdcdcdhd}\\
(((r1\_int\_1~X0~(k4\_xcmplx\_0~X1)){\unicdbdjdcd}(r1\_int\_1~(k4\_xcmplx\_0~X0)~X1)){\unicdcdcdhd}\\
((r1\_int\_1~(k4\_xcmplx\_0~X0)~X1){\unicdbdjdcd}(r1\_int\_1~X0~(k4\_xcmplx\_0~X1)))))))))))\end{array}
\label{hyp:ehbdadpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{{k1\_int\_2}~{X0}}={{k16\_complex1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(((r1\_xxreal\_0~k6\_numbers~X0){\unicdbdjdcd}(k16\_complex1~\\
X0=X0)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~k6\_numbers~X0){\unicdbdjdcd}(k16\_complex1~X0=k4\_xcmplx\_0~\\
X0)))\end{array}
\label{hyp:egbdpfbgcgdhghbgmgfhfg}
\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:mgfdfdpfhhdhjgfgchahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}((r1\_int\_1~\\
X0~X1){\unicdbdjded}(r1\_int\_1~X0~(k1\_int\_2~X1))))\end{array}$$
\end{theorem}
\end{document}
