\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{t47\_complsp2 (TMUwrs1HLokvEHujmcSpMA9fHTxhLDexHDw)}
\maketitle
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_seq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_finseq\_1~X0~k2\_numbers){\unicdcdcdhd}(m1\_finseq\_1~\\
X1~k2\_numbers)){\unicdbdjdcd}(k9\_seq\_4~X0~X1=k1\_valued\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\\
v3\_valued\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0)))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v3\_valued\_0~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))))){\unicdbdjdcd}(k4\_rvsum\_1~X0~X1=\\
k1\_valued\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfchghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))\end{array}
\label{hyp:egehpfngbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_finseq\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v3\_valued\_0}~{X0}})}}}\label{hyp:dgdgedpfdhfgbhngpfdd}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfdgpgngahmgdhahcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_1~X3~k1\_numbers){\unicdbdjdcd}(((X0=X2){\unicdcdcdhd}((X1=X3){\unicdcdcdhd}(k3\_finseq\_1~\\
X0=k3\_finseq\_1~X3))){\unicdbdjdcd}(k9\_seq\_4~X0~X1=k4\_rvsum\_1~X2~X3)))))\end{array}$$
\end{theorem}
\end{document}
