\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{t2\_series\_2 (TMQBpY3v3GY8kh2ELn7XN7nzuwCady1VQit)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_newton : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ np\_\_10 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((k1\_newton~(k2\_xcmplx\_0~X0~np\_\_1)~\\
np\_\_4=k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k1\_newton~\\
X0~np\_\_4)~(k3\_xcmplx\_0~np\_\_4~(k1\_newton~X0~np\_\_3)))~(k3\_xcmplx\_0~\\
np\_\_6~(k1\_newton~X0~np\_\_2)))~(k3\_xcmplx\_0~np\_\_4~X0))~np\_\_1){\unicdcdcdhd}(k1\_newton~\\
(k2\_xcmplx\_0~X0~np\_\_1)~np\_\_5=k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~\\
(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k1\_newton~X0~np\_\_5)~(k3\_xcmplx\_0~np\_\_5~\\
(k1\_newton~X0~np\_\_4)))~(k3\_xcmplx\_0~np\_\_10~(k1\_newton~X0~np\_\_3)))~\\
(k3\_xcmplx\_0~np\_\_10~(k1\_newton~X0~np\_\_2)))~(k3\_xcmplx\_0~np\_\_5~\\
X0))~np\_\_1))\end{array}
\label{hyp:mghdpfdhfgchjgfgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(k1\_newton~(k2\_xcmplx\_0~X0~np\_\_1)~\\
np\_\_3=k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k1\_newton~X0~np\_\_3)~\\
(k3\_xcmplx\_0~np\_\_3~(k1\_newton~X0~np\_\_2)))~(k3\_xcmplx\_0~np\_\_3~X0))~\\
np\_\_1)\end{array}
\label{hyp:mgfdpfdhfgchjgfgdhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfdhfgchjgfgdhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((k1\_newton~(k2\_xcmplx\_0~X0~np\_\_1)~\\
np\_\_3=k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k1\_newton~X0~np\_\_3)~\\
(k3\_xcmplx\_0~np\_\_3~(k1\_newton~X0~np\_\_2)))~(k3\_xcmplx\_0~np\_\_3~X0))~\\
np\_\_1){\unicdcdcdhd}((k1\_newton~(k2\_xcmplx\_0~X0~np\_\_1)~np\_\_4=k2\_xcmplx\_0~\\
(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k1\_newton~X0~np\_\_4)~(\\
k3\_xcmplx\_0~np\_\_4~(k1\_newton~X0~np\_\_3)))~(k3\_xcmplx\_0~np\_\_6~(k1\_newton~\\
X0~np\_\_2)))~(k3\_xcmplx\_0~np\_\_4~X0))~np\_\_1){\unicdcdcdhd}(k1\_newton~(k2\_xcmplx\_0~\\
X0~np\_\_1)~np\_\_5=k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~\\
(k2\_xcmplx\_0~(k1\_newton~X0~np\_\_5)~(k3\_xcmplx\_0~np\_\_5~(k1\_newton~\\
X0~np\_\_4)))~(k3\_xcmplx\_0~np\_\_10~(k1\_newton~X0~np\_\_3)))~(k3\_xcmplx\_0~\\
np\_\_10~(k1\_newton~X0~np\_\_2)))~(k3\_xcmplx\_0~np\_\_5~X0))~np\_\_1)))\end{array}$$
\end{theorem}
\end{document}
